(Adds Modi speaking to business council, analysts' quotes; details)
By Steve Holland and David Brunnstrom
WASHINGTON, Sept 30 (Reuters) - U.S. President Barack Obama and Indian Prime Minister Narendra Modi agreed on Tuesday to deepen U.S.-Indian cooperation on maritime security to ensure freedom of navigation in what amounts to a response to China's naval muscle-flexing in Asia.
The agreement emerged from two days of talks between Obama and the new Indian prime minister as they worked to revitalize a relationship hurt by a heated diplomatic dispute at the turn of the year and flagging optimism about India as a place to do business before the reform-minded Modi came to power in May.
Obama and Modi, speaking to reporters in the Oval Office, said their discussions ranged from trade to space exploration to climate change to the Islamic State threat in the Middle East.
"We already have the foundation of a strong partnership," said Modi, seated beside Obama. "We now have to revive the momentum and ensure that we get the best out of it for our people and for the world."
Modi received a warm welcome in the United States, even though he was denied a visa in 2005 over rioting in his home state three years earlier that killed more than 1,000 people, mostly Muslims. Modi, a Hindu nationalist, was exonerated by an Indian Supreme Court investigation.
A stronger relationship between the United States and India, the world's two largest democracies, has the potential to provide a counterweight to China, whose maritime moves in the Asia-Pacific have rattled regional nerves.
A joint statement said Obama and Modi agreed "to intensify cooperation in maritime security to ensure freedom of navigation and unimpeded movement of lawful shipping and commercial activity, in accordance with accepted principles of international law."
China's increasing assertiveness over territorial claims in the South China Sea and East China Sea has angered its neighbors. India and China have a long-running land border dispute and India's military has recently been monitoring Chinese activity in the Indian Ocean.
Obama and Modi also agreed to negotiate a 10-year extension of a military cooperation framework due to expire at year-end, and will stress counter-terrorism cooperation and joint efforts against militant networks.
However, Indian officials noted that while terrorism was a big shared concern, the joint statement made no reference to any plan for India to joint Obama's coalition against the Islamic State.
NO BIG BREAKTHROUGHS
While the leaders did not announce big-ticket agreements or breakthroughs in resolving significant trade and business irritants, the visit amounted to an official clearing of the air after Modi's visa issue and India's outrage at the arrest in New York last year of one of its diplomats, who was charged with visa fraud and paying her nanny less than the minimum wage.