At the conclusion of about two hours of talks, Obama said he and Prime Minister Manmohan Singh had agreed to "work even closer" on sharing information between law enforcement and intelligence agencies. Singh promised increased cooperation with Washington to battle terrorism.
Obama was quizzed about the tense relationship between India and Pakistan and said it was not the role of the United States to intervene and solve such problems. He said, however, that American should do what it can to ensure that Pakistan and India both feel secure and able to focus on developing their own countries for their own people.
On security, Obama said the U.S and India are natural allies.
"We both recognize that our core goal is to achieve peace and security for all peoples in the region, not just one country or the other," he said.
The two leaders glossed over a dispute about commitments to reduce greenhouse gases in advance of the next month's climate change summit in Copenhagen, but Obama said they had moved a "step closer" to a successful outcome.
Noting that the United States was India's largest trading partner, Obama said broadening trade ties would help create much needed jobs in both countries as governments continue trying to stimulate recession-hit economies.
In an elaborate welcoming ceremony earlier Tuesday, Obama showered praise on India and Singh, declaring it was only fitting the Indian leader should be the first state visitor of his administration.
Obama said the United States and India share the "bold experiments" of becoming democracies after breaking from rule by a colonial power, and in modern times both have known the pain of international terrorism.
"Our nations are two global leaders, driven not to dominate other nations but to build a future of security and prosperity for all nations," Obama said
Chilly, damp weather led the White House to move the ceremony indoors, where Singh and Obama stood before photographers and television cameras in the East Room as a Marine band played the national anthems of their countries.
Singh said that India and the U.S. are separated by distance but bound by common national values of "democracy, pluralism, rule of law and respect for fundamental human freedoms."
The White House was eager to show that, despite what some Indians see as a lack of attention during Obama's first 10 months, it values Singh's country as a key partner in dealing with extremists in South Asia, in settling international trade and global warming pacts and in steering the world economy out of turmoil.
Indians were looking for Obama to reverse a perception that he neglected India during his recent trip to Asia and seemed to endorse a stronger role for China in India's sensitive dealings with Pakistan.
Obama words sought to re-establish the strong feelings of goodwill the countries enjoyed during George W. Bush's presidency. Bush is credited with transforming the relationship after decades of Cold War-era distrust.
The symbol of those new ties is a civilian nuclear cooperation accord signed into law last year after years of close communication and tough negotiation. Obama voiced his commitment to the accord, which has raised hackles in Pakistan, India's bitter rival and a country the United States relies on in the fight against extremists along the Pakistan-Afghanistan border.
The two leaders were expected to have a memorandum intended to improve cooperation on energy security, clean energy and climate change, but there were no immediate details.
Developing and industrialized countries have bickered as they prepare to negotiate a new global climate change treaty in Copenhagen, meant to replace the 1997 Kyoto Protocol on carbon dioxide emissions.
Developing countries argue that rich countries produced most of the heat-trapping greenhouse gases on their march to development and should therefore bear the costs of fixing the problem. Wealthy nations say all countries - including large polluters India and China - have to agree to broad cuts in emissions.
India is willing to work on any climate solution that does not hurt developing countries' efforts to lift their populations out of poverty, Singh said before meeting Obama.