"The President invited Narendra Modi to visit Washington at a mutually agreeable time to further strengthen our bilateral relationship," the White House said following the maiden telephonic conversation between the two leaders.
The phone call was stated to be brief.
Modi, during his US visit would be eligible for an A-1 visa, State Department Spokesperson Jen Psaki said.
"The Prime Minister of India will be welcomed to the United States. As Head of Government, Modi would be eligible for an A-1 visa," she said.
Full Coverage:Lok Sabha Elections 2014
In 2005, the US State Department had revoked a visa that Modi had for traveling to the US on the ground of alleged human rights violations after the 2002 Gujarat riots.
The US has repeatedly said there is no change in its long-standing visa policy relating to Modi but he is free to apply for a visa and await a review like any other applicant.
During the call, Obama felicitated Modi on the BJP's success in India's historic election.
"The President noted he looks forward to working closely with Modi to fulfill the extraordinary promise of the US-India strategic partnership and they agreed to continue expanding and deepening the wide-ranging cooperation between our two democracies," the White House said.
Soon after the call, National Security Advisor Susan Rice wrote on Twitter - the micro blogging site - that the US looks forward to working with India to continue to build a strong partnership between the two largest democracies of the world.
"We congratulate Narendra Modi and the BJP on its victory in winning a majority of seats in India's historic national election, which saw more voters cast their ballots freely and fairly than in any election in human history," White House Press Secretary Jay Carney told reporters.
Secretary of State John Kerry offered his congratulations through twitter and said that he looks forward to working with the BJP on expanding their shared prosperity and security.
State Department Spokesperson said, "Once a new government is formed, we look forward to working closely with the Prime Minister and the Cabinet to advance our strong bilateral partnership."
"As President Obama said in his statement on May 12, we also congratulate the people of India on concluding their national elections and look forward to continuing our strong partnership based on shared values," the spokesperson said.