Ending a decade long US boycott of Narendra Modi, President Barack Obama congratulated him on BJP's "success in India's historic election" and invited him to visit Washington "to further strengthen our bilateral relationship".
"The president called prime ministerial candidate and Chief Minister of Gujarat Narendra Modi today to congratulate him on the Bharatiya Janata Party's success in India's historic election," said a White House readout of the call.
"The president noted he looks forward to working closely with Mr. Modi to fulfil 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 president invited Narendra Modi to visit Washington at a mutually agreeable time to further strengthen our bilateral relationship," the readout said.
In a separate statement, the State Department set at rest the issue of a visa for Modi saying: "The prime minister of India will be welcomed to the United States. As head of government, Mr. Modi would be eligible for an A-1 visa."
"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," department spokesperson Jen Psaki said in a statement.
Secretary of State John Kerry has also offered his congratulations, and looks forward to "working with the BJP on expanding our shared prosperity and security".
"We understand the next steps are for the Indian Election Commission to officially inform the president of the certified election results, and for him to appoint a prime minister.
"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," Psaki said.