NEW DELHI (AFP) - Indian Prime Minister Narendra Modi on Friday accepted an invite to meet US President Barack Obama in Washington in September, a statement said, as the two countries look to rebuild strained relations.

US Deputy Secretary of State William Burns formally invited Modi during a meeting between the pair in New Delhi on Friday, as part of a two-day visit to India to strengthen diplomatic and trade ties.

"Prime minister thanked President Obama for the invitation and looked forward to a result-oriented visit with concrete outcomes that imparts new momentum and energy to India-US strategic partnership," a statement from Modi's office said.

Modi considered that strengthening India-US relations "would send an important message to the region and beyond", the statement said.

Modi had been widely tipped to meet Obama in September when he travels to the US for the UN General Assembly meeting in New York, after the president extended his invite by phone in May.

Modi was controversially refused a visa to visit the US in 2005 over allegations he turned a blind eye or worse to deadly anti-Muslim riots three years earlier in Gujarat state which he was then running.

But US and European governments have been rushing to court Modi since his right-wing party swept to power in May on a pledge to reform the Indian economy, including by hiking foreign investment.

US Secretary of State John Kerry is expected in New Delhi at the end of July, while Modi met US Senator John McCain last week.

That meeting came one day after India summoned the top diplomat from the US embassy to complain for the third time about spying, following new allegations that Washington's National Security Agency targeted its ruling party.

A classified document made public showed that Modi's Bharatiya Janata Party was among authorised targets for the NSA in 2010 while it was India's main opposition.

Burns acknowledged the "seriousness of the concerns that have been raised" but refused any further comment.

"I am simply not in a position to comment publicly on those specific allegations," he said Friday in an interview with NDTV news channel.

India-US relations are also recovering from a major dispute in December over the arrest and strip-search of an Indian diplomat in New York, over claims that she mistreated a domestic servant, a move that sparked fury in India.