Obama: US and India can be 'best partners'
US President Barack Obama has said his country can become India's "best partner" as he concludes a landmark three-day visit to Delhi.
But he stressed that climate change could not be reversed unless India embraced cleaner fuels.
Mr Obama was addressing an audience largely made up of students at a town hall meeting in India's capital.
He said on Monday there was "much untapped potential" in the US-Indian economic relationship.
Some 2,000 people - mostly students and one of this year's two Nobel Peace Prize winners, Indian child rights activist Kailash Satyarthi - cheered wildly as President Obama described relations between the two countries as the defining partnership of the 21st Century, says the BBC's Sanjoy Majumder in Delhi.
"India and the United States are not just natural partners - I believe that America can be India's best partner," Mr Obama said.
"Of course, only Indians can decide India's role in the world. But I'm here because I am absolutely convinced that both our peoples will have more jobs and opportunity, our nations will be more secure, and the world will be a safer and more just place when our two democracies stand together."
But President Obama warned that the world does not "stand a chance against climate change" unless developing countries like India reduce dependence on fossil fuels.
He also spoke of the importance of religious tolerance and raised the issue of women's safety and dignity.
"In both of our countries, in all countries, upholding this fundamental freedom [of religion] is the responsibility of the government, but its also the responsibility of every person," President Obama said.
And he said "every woman should be able to go about her day - to walk the street, or ride the bus - and be safe and be treated with the respect and dignity that she deserves."
India has been criticised for its treatment of its women ever since a 23-year-old student was gang-raped and murdered on a bus in Delhi in December 2012.
Tuesday's town hall meeting took place at Delhi's Siri Fort Auditorium.
Mr Obama's three-day tour was aimed at boosting economic ties between the two major allies.
On Sunday, the first day of his visit, Mr Obama and Indian Prime Minister Narendra Modi announced a breakthrough on a pact that will allow US companies to supply India with civilian nuclear technology.
Analysis: Soutik Biswas, BBC News, Delhi
The historic 2006 India-US nuclear deal had been held up for eight years amid US concerns over who would be liable for any nuclear accident. Mr Singh, the deal's architect, had told the parliament that it marked the "end of India's decades-long isolation from the nuclear mainstream".
Now, a large insurance pool will be set up, without the need for any further legislation. The plan, according to reports, is to transfer the financial risk to insurers in the case of an accident.
Analysts say the two governments have done "all they can do" and it is now up to the suppliers - or American firms wanting to sell reactor technology to India - to do business.
At the business event on Monday evening, both he and Mr Modi hailed the bilateral progress, with the Indian leader saying a stronger relationship "will make this world a better place for all".
Mr Obama said trade had grown by around 60% in the past few years which was a "win-win" situation.
"We're moving in the right direction," he said. "That said, we all know that the US-India economic relationship is also defined by so much untapped potential."
Mr Obama's visit to India has been shortened so he can visit Saudi Arabia and pay his respects following the death of King Abdullah. It means he and his wife, Michelle, will not now visit the Taj Mahal.