"India has set an example for the world in holding the largest democratic election in history, a vibrant demonstration of our shared values of diversity and freedom," Obama said in a statement.
"We look forward to the formation of a new government once election results are announced and to working closely with India's next administration to make the coming years equally transformative."
Obama did not mention the Bharatiya Janata Party (BJP) under Hindu nationalist Narendra Modi, which exit polls suggest will emerge as the biggest party from polls in which more than 500 million people voted.
The United States had for years refused to deal with Modi over allegations he failed to swiftly curb deadly 2002 anti-Muslim riots in Gujarat which left at least 1,000 people dead shortly after he came to power as chief minister there.
Washington ended its boycott of Modi in February when Nancy Powell, the outgoing US ambassador to India, shook hands with him at the start of closed-door talks.
In 2005, the United States refused Modi a visa under a domestic law that bars entry to any foreign official seen as responsible for severe violations of religious freedom.
State Department spokeswoman Jen Psaki refused to discuss Modi's visa case.
Four out of five Indian exit polls released soon after the final ballots were cast Monday pointed to a narrow majority for the BJP, indicating a new government led by Modi was poised to take over.
That would inflict a humiliating defeat on the ruling leftist Congress party and its leaders, the Gandhi political dynasty.
Obama's White House made a big effort to court India early in his administration as part of his policy of rebalancing US diplomatic and military resources towards the dynamic Asia-Pacific region.
But relations were damaged last year when Indian diplomat Devyani Khobragade was arrested and strip-searched in New York on charges of underpaying her servant.
Khobragade returned to India under a deal, but prosecutors went ahead in March with a second indictment.
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