John McCain who met Narendra Modi here conveyed the keen desire in the US to work with him to revitalise the India-US strategic partnership.
Modi said he hoped for forward looking visit to the US in September this year to take the relationship to a new level.
"Prime Minister conveyed his desire to further deepen and expand the strategic partnership, based on our shared values and interests, sensitivity to each other's concerns and tangible progress across the full spectrum of bilateral relations," said a statement by the PMO.
Modi added that the success of democratic countries and their cooperation will advance peace, stability and prosperity in the world.
Both also discussed the situation in Iraq and Afghanistan.
"The Prime Minister expressed concern over the increased threat of terrorism across the world, and reiterated that the fight against terror should be a global priority for humanitarian forces," the statement added.
Narendra Modi and McCain talk of desire to "revitalise" India-US ties
Newly elected Indian Prime Minister Narendra Modi pushed for improving U.S. ties during a meeting with Senator John McCain in New Delhi on Thursday, as the two countries seek to patch up their differences and boost their economic relationship.
The treatment of an Indian diplomat arrested in New York in December triggered a serious spat between the two countries and was widely blamed for the resignation of the U.S. ambassador to India.
The Obama administration has been seeking to revive ties since Modi's election in May, seeing India as a key strategic counter-balance in Asia to an increasingly assertive China.
Modi "conveyed his desire to further deepen and expand the strategic partnership," a statement from the Indian government said.
It said that he hoped for a "forward looking, result-oriented visit" to the United States in September when he is due to attend the United Nations General Assembly in New York.
McCain, who told the Senate last week that Washington should seek to help India's economic and military development, spoke of high expectations about a new momentum in India's economic growth under the new government. There was no mention in the statement of defence deals.
Both governments have signalled they are keen to ramp up bilateral trade, which stands at about $100 billion annually and is considered to be below potential due to disputes over protectionism and intellectual property rights.
McCain's visit comes at an awkward time - just days after reports that the U.S. National Security Agency was authorised to spy on Modi's Bharatiya Janata Party in 2010, when the party was in the opposition.
On Wednesday, India's foreign ministry summoned a senior U.S. envoy in Delhi and said it had sought an assurance that the surveillance would not happen in the future.
The Indian government statement of their remarks released after the McCain-Modi meeting did not mention the snooping row.
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 U.S. advances and shown no resentment publicly.
In addition to discussing the situation in Iraq and Afghanistan, Modi emphasised that the fight against terror should be a global priority, the statement said.