Indian Prime Minister-elect Narendra Modi "will be welcomed" to the United States, the White House said on Friday.
Spokesman Jay Carney said President Barack Obama "does plan to reach out" to him soon.
In a statement, State Department spokeswoman Jen Psaki said Modi would get a visa to the United States once he takes office and forms a government. Modi was denied one several years ago.
Now, however, Modi would be eligible for an A1 visa, said Psaki. Heads of government use such visas to travel to the United States.
"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," Psaki's statement said. "Secretary Kerry has also offered his congratulations, and looks forward to working with the BJP on expanding our shared prosperity and security."
Modi's Hindu nationalist Bharatiya Janata Party appears to have captured a landslide victory and he will likely become 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," the State Department statement said.
In 2005, the United States denied Modi a visa because of his alleged role in anti-Muslim violence three years earlier in Gujarat state, where he was chief minister.
More than 1,000 people were killed, mostly Muslims. A Supreme Court-ordered investigation in India absolved him of blame last year.