He also dismissed as 'petty nonsense' a news report that he had called the president a 'moron' during a tense meeting with national security officials this summer.
The White House and State Department commemorate other religious traditions, including a Jewish Passover Seder, as well as Christmas and Easter holidays.
Tillerson said that he believed that the US has a partner in Pakistan.
'We appreciate his positive evaluation of the relationship and share his optimism about its future directions.' 'We look forward to welcoming him in India next week for detailed discussions on further strengthening of our partnership,' the MEA said on Friday.
During his brief visit, Tillerson was given a tour of the room at the Birla House where Gandhi had spent his last 144 days.
"We want to work closely (with) Pakistan to create a more stable and secure Pakistan as well," he said.
Swaraj and Tillerson discussed a wide range of bilateral issues, including the situation in the neighbourhood and the Indo-Asia Pacific region, officials said.
Trump said he 'won't fail' on a front where three of his predecessors -- Clinton, Bush and Obama failed.
Trump also announced the appointment of Gina Haspel to head the Central Intelligence Agency -- the first woman selected for the agency's top post.
Senators said Pak's discriminatory laws continue to result in prosecution of individuals due to their faith.
Tillerson, 64, who was confirmed by the Senate in a 56-43 vote, was administered the oath of office by Vice President Mike Pence.
Pakistan Prime Minister Shahid Khaqan Abbasi assured the Secretary of State that his country is committed to the war against terrorism.
The issues that figured prominently in these discussions included terrorism, Afghanistan and the situation in the Asia Pacific region.
Tillerson said China's behaviour and action is "posing a challenge to the rules-based international order".
Tillerson said he hoped that at some point the North Koreans will begin to understand that the US would like to sit and have a dialogue with them.
During her week-long stay, Swaraj, leading a high-powered Indian delegation, is expected to hold about 20 bilateral and trilateral meetings with leaders attending the session.
Secretary Tillerson met with Foreign Secretary Jaishankar on Friday to discuss the US-India relationship and the agenda for Prime Minister Modi's meetings at the White House on June 26, a State Department spokesman said told PTI.
Tillerson said the US will provide India with best technologies for its military modernisation which include offers to supply F-16 and F-18 fighter jets.
The US Secretary of State said the two countries should find ways as to how they could work together to bring stability and peace to the whole region.
Chinese President Xi Jinping on Sunday vowed to work with the United States for healthy and stable development of bilateral ties, calling cooperation the "correct" choice for both the countries.
Tillerson is a veteran chief executive who has had extensive overseas business dealings but his relationships with foreign leaders could complicate his confirmation prospects.
Propelled to the position of the Secretary of State to "undo" years of American foreign policy "blunders and disasters", ExxonMobil CEO Rex Tillerson now faces the biggest challenge of his life to translate his business acumen to international diplomacy.
Secretary of State Rex Tillerson has told Pakistan that it must take action against terrorist groups and dismantle their safe havens on its soil.
More than 600,000 Rohingyas from Myanmar's Rakhine state have fled to neighbouring Bangladesh, creating one of the world's most dire refugee crisis.
United States President Donald Trump's administration has been marked by a series of exits from high-ranking officials. Appointments expected to last for years have only made it a matter of days, ending in chaotic departures. On March 23, adding to the long list of departures from the US administration was National Security Adviser Lt General H R Mcmaster who will be replaced by John Bolton. Here's a list of other notable departures from Trump's White House.
Tillerson, is currently on top of the list of Trump's Secretary of State because of his contacts with the world leaders, in particular Russian President Vladimir Putin, media reports said.
The United States identified LeT as one of the largest and most active terrorist organisations in South Asia.
The White House has maintained that this is "not the time to talk" to North Korea, which has been carrying out ballistic missile test.
North Korea conducted a ground test of a new type of high-thrust rocket engine on Saturday.
'We have put people on notice that if you're harbouring terrorists, be warned, be forewarned that we're going to engage with those who are providing safe haven and ask them to change what they're doing.'
Earlier, United States Secretary of State Rex Tillerson urged the international community to increase pressure on North Korea, saying that failing to do so would bring 'catastrophic consequences'.
North Korea had recently called on its citizens to be ready for a nation-wide struggle against 'war thirsty' Trump.
Mattis also warned Pakistan of global "diplomatic isolation" and losing its Non-NATO ally status if it failed to take action against safe havens to terrorists on its soil.
The IAF chief has said that his force had the capability of locating, fixing and striking across the border.
A top American diplomat has said asserting that the Trump Administration is moving quickly on its own strategy to fight against terror groups.
The US Pacific Command said the missiles appeared to be short-range. The first and second missiles "failed in flight" and the third "appears to have blown up almost immediately".
US intelligence agencies had been tracking the hostages and shared their location when they were shifted to Pakistan.
The former Central Intelligence Agency director, was confirmed by the Senate by 57-42 votes. He replaced Rex Tillerson, who was fired by US President Donald Trump last month.
'It is an unpleasant fact of history that stronger nations dominate the power play and the only way it can be mitigated is through recourse to diplomacy,' says Ambassador M K Bhadrakumar.
The leaders were accompanied by US Secretary of State Rex Tillerson and Russian Foreign Minister Sergey Lavrov at the bilateral meeting.
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