Washington also pledged to work with "the leaders chosen by the Indian people," State Department spokeswoman Jen Psaki said, as exit polls tipped a win for the Bharatiya Janata Party (BJP) under Narendra Modi, who was long boycotted by the US until earlier this year.
India had organised "the largest-ever free and fair democratic election in human history," Psaki told reporters.
The polls were "an inspiring example of the power of the democratic process in action, and the United States, like so many others around the world, has great admiration and respect for the vibrancy, diversity and resilience of India's democracy."
That would inflict a humiliating defeat on the ruling Congress party and its leaders, the Gandhi political dynasty.
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But Modi, who was boycotted by both the United States and the European Union for a decade, remains a deeply polarising figure over allegations he failed to curb swiftly deadly 2002 riots in Gujarat which left at least 1,000 people dead shortly after he came to power as chief minister there.
In 2005, the US had refused Modi a visa under a domestic law that bars entry to any foreign official seen as responsible for "severe violations of religious freedom."
But Psaki today refused to discuss his visa case, saying only: "We look forward to working with the leaders chosen by the Indian people to advance this important partnership and to set an ambitious agenda.