The Obama administration has been working to boost ties since Modi's thumping election victory, seeing India as an important counterweight to an increasingly assertive China and a prospective export market.
Deputy Secretary of State William Burns delivered a written invitation from Obama to Modi on Friday, the Indian government said in a statement.
Obama's letter reiterated earlier invitations. "We recognise the very strong mandate that he's won and we have a deep interest and stake in his success, in India's success," Burns told Indian news channel NDTV, adding that the meeting with Obama was likely to take place on September 30.
Modi's Bharatiya Janata Party won an outright majority in India's parliament in May, something no party has managed for three decades, ousting the Congress party that has long dominated politics.
India and the United States set great store by the economic potential of their ties, but their relationship has been fraught in recent years. Washington has set a strategic goal of expanding their $100 billion annual trade by five times.
In its statement, the Indian government said Modi was "looking forward to a result-oriented visit with concrete outcomes that impart new energy to (the) India-US strategic partnership".
A spokesman for the Ministry of External Affairs confirmed that Modi had formally accepted Obama's invitation.
Modi was denied a visa in 2005 for travel to the United States following religious riots in 2002 while he was a state chief minister. Even so, he has responded positively to the US advances and shown no resentment publicly.
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@amir jafri:Truly said Mr Amir.The only thing British did to destroy a country is to make those people hate their own culture first and dump them.They were successful on that.
@Aseem: Even Umar Riaz Abbasi of Qadri's Party (PAT) praises Modi lavishly on Pakistan's TV channels. Watch "11th hour - July 8, 2014" He says that Modi is taking more care of the muslims of India than Pakistan. He said that India's hindu Prime Minister Modi distributed free to muslims during Ramzan 45000 tons of rice, value of which is INR.30 crores (INR.300 million) during Ramzan. He asked if Pakistan has done any such thing and asked Pakistan to learn from India's Hindu Prime Minister Modi.
People who make decisions on superficial and hypothetical points, have to change their mind time to time. Modi's humbleness that he accepted Invitation. Modi's humbleness that he invited neighbors. He is thinking Nation first, not Modi first !
such respect is accorded only to those who speak Desi, eat Desi, and dress Desi. Unl;ike the english-medium O/A level slaves of Pakistan....whose only pride is that "they know only little little" Urdu.
Obama wants to meet Modi, Angela Merkel is keen to meet Modi, Shinzo Abe is waiting for the bilateral summit with Modi... Both Germany and Japan want to come out of self imposed isolation from geo politics and are keen to play major roles now. A new Axis is emerging.