Russian ambassador to the United States Anatoly Antonov warned that such actions will not be left without consequences.
The White House said it has 'a large body' of evidence indicating that the Assad regime was responsible for the April 7 chemical attack in Duma.
British PM Theresa May said there was no alternative to military action.
In a combined operation, the United States, Britain and France on Saturday launched military strikes against Bashar al-Assad’s Syrian regime, President Donald Trump announced, as he alleged the war-torn nation of using chemical weapons against its own people.
The 'precise, overwhelming and effective' military strike was aimed to 'cripple' the chemical weapons infrastructure of the Syrian regime and it succeeded in destroying three chemical weapons facilities in the war-torn country, the Pentagon said.
It said the 'precise, overwhelming and effective' military strike in Syria by the US, France and Britain were intended to send a clear message that the use of chemical weapons against its own civilians is inexcusable.
The Pentagon said it destroyed three chemical weapons facilities of the Syrian regime.
Marine Lt Gen Kenneth F McKenzie director, Joint Staff, told reporters that the US, France and Britain in all deployed 105 missiles against three targets.
"Taken together were able to overwhelm the Syrian air defence system," he said.
Soon after the strikes were launched, Russian ambassador to the United States Anatoly Antonov warned that such actions will not be left without consequences.
Antonov released a statement on Twitter saying, 'A pre-designed scenario is being implemented. Again, we are being threatened. We warned that such actions will not be left without consequences.'
He further noted that all responsibility for strike rests with Washington, London and Paris while adding that the 'US, the possessor of the biggest arsenal of chemical weapon has no moral right to blame other countries'.
Denouncing the strikes as 'brutal, barbaric aggression' that violated international law, Syria's government said, "The Syrian Arab Republic condemns in the strongest terms the brutal American-British-French aggression against Syria, which constitutes a flagrant violation of international law."
Assad said Western strikes on government military installations only made him keener to fight back against his opponents, in comments published by his office.
"This aggression will only make Syria and its people more determined to keep fighting and crushing terrorism in every inch of the country," Assad, in his first reaction to the strikes, told his Iranian counterpart Hassan Rouhani.
The US president claimed that the joint action was meant to establish a 'strong deterrent' against the production, spread, and use of chemical weapons.
In his first reaction after militaries of the three countries carried out the strikes, Trump declared 'Mission Accomplished'.
'A perfectly executed strike last night. Thank you to France and the United Kingdom for their wisdom and the power of their fine Military. Could not have had a better result. Mission Accomplished!' Trump said in a tweet today.
'So proud of our great military which will soon be, after the spending of billions of fully approved dollars, the finest that our country has ever had. There won't be anything, or anyone, even close!' tweeted the US President.
Earlier in the day, Trump said he has ordered 'precision strikes' against Syria, where dozens of people were killed last weekend in a suspected toxic gas attack on Douma, the largest town in a former rebel stronghold outside Damascus.
"These are not the actions of a man; they are crimes of a monster instead," Trump said in an address to the nation.
"America does not seek an indefinite presence in Syria," he said, thanking the UK and France for joining the US in its fight against the Syrian regime.
"My fellow Americans, a short time ago, I ordered the United States armed forces to launch precision strikes on targets associated with the chemical weapons capabilities of Syrian dictator Bashar al-Assad. A combined operation with the armed forces of France and the United Kingdom is now underway. We thank them both," Trump said in his address to the nation.
"Today, the nations of Britain, France, and the United States of America have marshaled their righteous power against barbarism and brutality," Trump said.
He attacked the Assad regime for 'deploying chemical weapons to slaughter innocent civilians', referring to the alleged atrocity in Douma last Saturday.
"This massacre was a significant escalation in a pattern of chemical weapons use by that very terrible regime," Trump alleged.
"The evil and the despicable attack left mothers and fathers, infants and children, thrashing in pain and gasping for air. These are not the actions of a man; they are crimes of a monster instead," he said.
The US president sought to bring back the vestiges of World War I, after which civilised nations joined together to ban chemical warfare.
He noted that chemical weapons not only inflict gruesome suffering but also even small amounts of them can unleash widespread devastation.
"The purpose of our actions tonight is to establish a strong deterrent against the production, spread, and use of chemical weapons. Establishing this deterrent is a vital national security interest of the United States,” Trump said.
"The combined American, British, and French response to these atrocities will integrate all instruments of our national power -- military, economic, and diplomatic. We are prepared to sustain this response until the Syrian regime stops its use of prohibited chemical agents,” he said.
Trump said he also has a message for the two governments most responsible for supporting, equipping, and financing the criminal Assad regime.
"To Iran, and to Russia, I ask: What kind of a nation wants to be associated with the mass murder of innocent men, women, and children?” he asked.
"The nations of the world can be judged by the friends they keep. No nation can succeed in the long run by promoting rogue states, brutal tyrants, and murderous dictators,” he said.
Trump said Assad’s recent attack was a fallout of Russia’s “failure” to keep the promise of eliminating Syria’s chemical weapons.
"In 2013, President Putin and his government promised the world that they would guarantee the elimination of Syria’s chemical weapons. Assad’s recent attack are the direct result of Russia’s failure to keep that promise,” Trump said.
"Russia must decide if it will continue down this dark path, or if it will join with civilised nations as a force for stability and peace. Hopefully, someday we’ll get along with Russia, and maybe even Iran -- but maybe not,” he said.
The US president said America, being the world’s greatest and most powerful economy, has a lot to offer.
"In Syria, the United States -- with but a small force being used to eliminate what is left of Islamic State -- is doing what is necessary to protect the American people. Over the last year, nearly 100 per cent of the territory once controlled by the so-called ISIS caliphate in Syria and Iraq has been liberated and eliminated," he said.
British Prime Minister Theresa May said that she had authorised British forces to conduct precision air-launched cruise missile strikes on Syria to degrade its chemical weapons capability, saying there was no alternative to military action.
Four Royal Air Force Tornado jets using Storm Shadow missiles had taken part in the attack on a military facility near Homs where it was assessed Syria had stockpiled chemicals, Britain's Ministry of Defence said.
Defending the joint air strikes, the White House said it has ‘a large body’ of evidence indicating that the Assad regime was responsible for the April 7 chemical attack in Duma and that Syrian military officials coordinated the attack.
The White House released an information sheet making its case for the Syrian regime's involvement in the Duma attack.
‘A large body of information indicates that the Syrian regime used chemical weapons in the Duma area of East Ghutah, near Damascus, on April 7, 2018. Our information is consistent and corroborated by multiple sources,’ the White House statement said.
‘This conclusion is based on descriptions of the attack in multiple media sources, the reported symptoms experienced by victims, videos and images showing two assessed barrel bombs from the attack, and reliable information indicating coordination between Syrian military officials before the attack,’ the White House assessment said.
According to the White House Assad regime’s continued use of chemical weapons threatens to desensitise the world to their use and proliferation, weaken prohibitions against their use, and increase the likelihood that additional states will acquire and use these weapons.
‘To underscore this point, not only has Russia shielded the Assad regime from accountability for its chemical weapons use, but on March 4, 2018, Russia used a nerve agent in an attempted assassination in the United Kingdom, showing an uncommonly brazen disregard for the taboo against chemical weapons,’ the White House alleged.
‘A significant body of information points to the regime using chlorine in its bombardment of Duma, while some additional information points to the regime also using the nerve agent sarin. This is not an isolated incident -- the Syrian regime has a clear history of using chemical weapons even after pledging that it had given up its chemical weapons program,’ it said.
The US assesses that the Syrians fired about 40 missiles in retaliation, but none of them endangered the US forces and its allies. Defensive effort of Syria was ineffective, Lt Gen Kenneth F McKenzie said.
The Syrian regime had a pattern of using chemical weapons against the chemical weapons convention, alleged the Pentagon Chief Spokesperson Dana White.
"This is a heinous regime, which murders its people daily," she said.
It was a deliberate decision to the target the storage and research and development facilities, she said.
"We are confident that we have significantly degraded the ability to ever use the chemical weapons again," White said, asserting that the US policy on Syria has not changed.
"Our mission in Syria remains the same, to defeat the Islamic State and not be involved in the civil war," White said, adding that the US is 100 per cent behind the Geneva peace process.
The new UN envoy provides an opportunity for everyone to work towards a Syrian peace process.
"We are confident that the UN process will move forward," White told reporters in response to a question.
"We took action. What happens next is in the hands of Assad," she said.
The US did no coordination with the Russians, McKenzie said.
Responding to questions, he said it is possible that some people might have left from the strike facilities. The strikes were carried out in the week hours of the morning (3 am-4 am) so as to reduce the possibility of any civilian casualty.
The US believes that the material and equipment at the source of this site was not movable.
"This is far more damaging to Syria," he said.
Responding to questions, White said this was a fully legitimate operation and the President had the authority to order conducting these strikes.
"It was a successful mission. What happens next depends on what the Assad regime decides to do," she said.
The Republican party lawmakers hailed President Trump for his decision to carry out the strikes, while the Democrats sought action against Russia, alleging that Moscow was behind the Assad regime's ‘atrocities’ against his own people.
‘Applaud’ Trump for taking military action against the Assad regime for its latest use of chemical weapons, and for signalling his resolve to do so again if these heinous attacks continue, said Senator John McCain, Chairman of the powerful Armed Services Committee.
McCain said the message to Assad must be that the cost of using chemical weapons is worse than any perceived benefit.
However, Democratic leader Nancy Pelosi said that one night of air strikes was not a substitute for a clear, comprehensive Syria strategy.
"The President must come to Congress and secure an Authorisation for Use of Military Force by proposing a comprehensive strategy with clear objectives that keep our military safe and avoid collateral damage to innocent civilians," she said.
"President Trump must also hold Putin accountable for his enabling of the Assad regime's atrocities against the Syrian people," Pelosi said.
House Speaker Paul Ryan said the US had taken decisive action in coordination with its allies.
"We are united in our resolve that Assad's barbaric use of chemical weapons cannot go unanswered. His regime's unconscionable brutality against innocent civilians cannot be tolerated," he said.
"There should be no doubt that Russia and Iran have blood on their hands, and their partnership with Assad reveals the true nature of their regimes. The United States and our allies must continue to seek ways to hold Assad's enablers accountable," Ryan said.
The administration is justified to take limited action in coordination with its allies to hold Assad accountable for the use of chemical weapons, said Congressman Ed Royce, Chairman of the House Foreign Affairs Commitee.
Indian-American Congresswoman Pramila Jayapal said Trump has just conducted another set of unconstitutional strikes.
"He does not have the power to take these actions without consulting Congress. Only Congress – not the White House – has the power to declare war," she said.
"Tonight's air strikes are not a long term plan to resolve the Syrian crisis, and they will do little to stop a dictator like Assad from repeating his crimes against humanity," she said.
"We need a considered, debated, real strategy to end the violence in Syria and protect innocent people from dying. These air strikes are not only unconstitutional, they are dangerously escalating a conflict that could send us into a war with multiple countries," Jayapal said.
"This is a debate that must take place in Congress immediately, and we should be clear that the President has exceeded the authority afforded to him by the Constitution," she added.
China opposed the joint attack, saying any action bypassing the United Nations charter violates the principles of international law and the basic norms governing international relations.
Calling for the relevant parties to return to the framework of international law and resolve the Syria issue through dialogue and negotiation, Chinese Foreign Ministry spokesperson Hua Chunying said Beijing is opposed the use of force.
"China opposed the use of force in international relations and called for respect for other countries' sovereignty, independence and territorial integrity," she said in response to media queries, seeking Beijing reaction to the air strikes.
"Any unilateral military action bypassing the Security Council runs contrary to the purpose and principles of the United Nations (UN) Charter and violates the principles of international law and the basic norms governing international relations, and will further complicate the Syrian issue," Hua said.
Hua said China believes a comprehensive, impartial and objective investigation should be carried out to reach a reliable conclusion that could stand the test of time.
"Yet before that, a prejudgment should not be made," she added.
China believes that political settlement is the only viable way out for the Syrian issue. Relevant parties of the international community should continue to support the role of the UN as the main channel for mediation and make relentless efforts to facilitate the final settlement of the Syrian issue.
Iran's supreme leader Ayatollah Ali Khamenei denounced Trump, France's President Emmanuel Macron and May, branding them 'criminals'.
"The attack this morning against Syria is a crime," Khamenei said in remarks published on his Telegram channel. "The American president, the French president and the British prime minister are criminals."
Turkey welcomed Western strikes as an 'appropriate response' in retaliation for a suspected chemical attack that left dozens dead.
'We welcome this operation which has eased humanity's conscience in the face of the attack in Douma, largely suspected to have been carried out by the regime,' the Turkish foreign ministry said in a statement.
'The Syrian regime, which has been tyrannising its own people for more than seven years, be it with conventional or chemical weapons, has a proven track record of crimes against humanity and war crimes,' the ministry said.