"I think our relationship between the United States and India is so strong and enduring we won't worry about the Twitter rank order," State Department Spokesperson Jen Psaki told reporters at her daily news conference.
"Obviously, we have a long, enduring partnership with India. That will continue, and hopefully only grow in the future," Psaki said while responding to a question on whether the US is bothered that President Barack Obama was so far down on the list of Modi's priorities.
While responding to congratulatory messages from world leaders such as Russian President Vladimir Putin and others, Modi had mentioned the name of Obama very late in his tweets.
"In our conversation, @BarackObama & I talked about further strengthening India-USA strategic partnership that will help both nations," Modi wrote on Twitter.
Modi also responded to the congratulatory message he received from Secretary of State John Kerry.
"Thank you Mr Kerry. We will strengthen relations between our 2 (two) vibrant democracies in the years to come," Modi said in his first public comment on India-US relationship after the election results were declared.
Psaki said Modi, who has been invited to Washington by Obama, is welcome to travel to the US and in his capacity as the head of a State would receive A1 visa.
"Heads of government and heads of state are eligible for an A-1 visa and must travel to the United States on an A-1 visa regardless of the purpose of the trip. As Prime Minister of India, obviously Modi would be a head of state.
"And you saw the announcement from the White House this weekend after the president's call that they've invited him and would welcome him to the United States," Psaki said.
The US, she said, has a "very important strategic relationship" with India and a range of US officials in New Delhi interact with the Indian government depending on the issue.
"I expect there'll be a range of officials who will be in touch with the new government and be working with them," she said.
Modi has had an uneasy relationship with the US which denied him a visa in 2005 over 2002 Gujarat riots. He has, however, in his public utterances stressed that foreign relations cannot be "influenced" by incidents related to individuals.