Trump also said he is "very disappointed" that India would be buying "so much oil" from Russia.
Tensions between the United States and Russia have reached new heights amid the ongoing Ukraine conflict, with a series of developments marking a dangerous escalation.
Lavrov, who addressed the UN General Assembly shortly before External Affairs Minister S Jaishankar's speech at the high-level General Debate, said India and Russia share a "particularly privileged strategic partnership".
Sullivan remarks come amid the rising friction between Washington and New Delhi due to the 50 percent tariffs imposed on Indian goods, which include a 25 percent penalty for buying Russian oil.
National Security Advisor Ajit Doval has travelled to Russia to hold crucial talks on bilateral energy and defence ties and to prepare ground for Russian President Vladimir Putin's visit to India later this year.
Describing the visit as "productive" in a post on X, the PM said he emphasised India's position on key global issues during his engagements.
His assertion came after Trump claimed that his "friend" PM Modi has assured him that India would stop purchasing oil from Russia, a move he described as a big step toward increasing pressure on Moscow over its invasion of Ukraine.
Russian Foreign Minister Sergei Lavrov on Thursday said the US threats of tariffs against India and China are failing and there is a growing understanding in Washington of the futility of talking in such language with two ancient civilisations.
Putin and Modi will discuss regional and global security, trade and all other topics on the agenda during their meeting, Peskov was quoted as saying by Russia's state-owned TASS news agency.
United States President Donald Trump has said there will be no trade negotiations with India until a dispute over tariffs is resolved, following his administration's decision to double tariffs on Indian imports.
"The two sides note that the relationship between Russia and China has progressed to a more advanced interstate cooperation compared to the military-political unions of the Cold War era as it is not bloc or confrontational in nature, nor does it target any third countries," Russia's new agency Tass quoted the document as saying.
Prime Minister Modi will hold in-person meetings with President Putin for 8-9 hours during his nearly 24-hour stay in Russia, they said.
Ahead of trade talks between Indian and United States officials in Delhi, White House trade advisor Peter Navarro said India, which has the 'highest tariffs' of any major country, is 'coming to the table'.
'Modi's a great leader... But I don't understand why he's getting into bed with Putin and Xi Jinping...'
The Ukrainian President's remarks come amid US President Donald Trump's criticism of India and China, labelling the countries as "primary funders" of the ongoing war in Ukraine.
Plans for big bang reforms in the GST regime by Diwali, the Putin-Trump summit and S&P upgrading India's sovereign credit rating are likely to instil optimism in the domestic equity market in the week ahead, analysts said. Besides, trends in global markets and the trading activity of foreign investors would also impact domestic investors' sentiment.
Echoing United States President Donald Trump's stance on imposing economic sanctions against countries maintaining trade ties with Russia if Moscow doesn't put an end to the conflict in Ukraine, North Atlantic Treaty Organisaiton (NATO) Secretary General Mark Rutte on Tuesday (local time) urged India, China, and Brazil to reconsider their economic relations with Russia, warning of potential secondary sanctions, reported Reuters.
US President Donald Trump claimed he resolved the India-Pakistan conflict earlier this year with trade and asserted that he should receive the Nobel Peace Prize for "ending seven wars."
Or is he training for the Olympics in Paris this July?
New Delhi 'will have to take a call which supply source suits us the best,' the finance minister said, pointing out that crude oil accounts for the bulk of India's foreign exchange spend.
The White House trade advisor's remarks came on a day US President Donald Trump announced that India and the US are continuing negotiations to address the trade barriers.
The US Department of the Treasury on Wednesday imposed sanctions on Russia's two largest oil companies, Rosneft and Lukoil, in an effort to pressure the Kremlin to end its war in Ukraine.
Putin received more votes in comparison to the 2018 elections where he bagged 76.69 per cent of the total votes counted. The performance of the other candidates was lower than that of the previous competitors of Russian President Vladimir Putin in 2018, according to reports.
The Indian government is dealing with the matter having in mind the national interests of this country in the first place, he said.
However, he suggested that Ukraine was also somehow involved.
India-US relations, like Rome, were not built in a day, nor can they be demolished in a day.
All said and done, when the new global order emerges, India can only remain with the democracies, asserts Ambassador T P Sreenivasan.
Both Putin and Zelenskyy have invited the prime minister to visit Russia and Ukraine respectively after the Lok Sabha elections, sources said, adding they see Modi as a "peacemaker".
Prime Minister Narendra Modi conveyed to Ukrainian President Volodymyr Zelenskyy that India remains committed to making every possible contribution for an early and peaceful solution to the conflict. Zelenskyy sought India's support in limiting Russian energy exports.
The trade relationship between India and the United States has been strained by the imposition of 25% tariff by the US on Indian goods.
Older Russians recall Mithun Chakraborty and the song Jimmy Jimmy Aaja from the movie Disco Dancer.
Glimpses from India and around the world that will make you smile and cry.
As the world continues to rage under the ongoing conflicts in Europe and the Middle East, the two presidential candidates in the United States, Vice President Kamala Harris and former President Donald Trump during the presidential debate hosted by ABC News on Tuesday (local time), presented their views on ending the conflict and Washington, DC's role in it.
US Secretary of State Marco Rubio has said that the Trump administration hopes it can fix the "measures" it has taken with regard to India for its purchases of Russian oil.
A meeting with Chinese President Xi Jinping on the sidelines of the SCO summit is being planned.
'Everybody in America loses because of what India is doing.'
After flying in by helicopter, Putin drove himself through the streets of Crimea and Mariupol according to reports and video footage.
India should simultaneously prioritise domestic exploration and production of more oil and gas in the country, and ensure we retain diversified suppliers for imports, points out former foreign secretary Ranjan Mathai.
'As one former Indian diplomat put it to me, Delhi has access to the White House, but Islamabad has access to Mar-a-Lago.'
Notably, US President Donald Trump and his administration have continuously targeted India over its purchase of Russian crude oil. India, on the other hand, has always maintained that India's purchases are based on its domestic needs and economic security.
