US President Barack Obama has pledged to work more closely with India to combat global terrorism.
He also offered to help India and Pakistan resolve their long-standing dispute over Kashmir, without intervening directly.
Speaking at a news conference alongside Indian prime minister Manmoham Singh, Mr Obama said that, while both India and Pakistan have an interest in reducing tensions in the region, the US "cannot impose a solution to these problems".
The conflict over Kashmir, a Muslim-majority Himalayan region where rebels have sought independence from India or incorporation with Pakistan, has been the main source of friction between the nuclear-armed neighbours since they won independence from Britain in 1947.
Pakistan has frequently sought outside intervention to resolve it but India vehemently opposes such involvement, and the United States has traditionally stayed above the fray. Mr Obama declined to veer from that stance.
Mr Singh said that, while he believed a strong, moderate Pakistan was in the interests of India and the wider region, India could not engage in talks as long as Pakistan's "terror machine is as active as ever before". However, he deflected a reporter's question about whether he would call Pakistan a terrorist state.
Mr Singh is seen as a driving force behind Indian efforts to make peace with Pakistan. He called off peace talks following the November 2008 Mumbai attacks, carried out by Pakistani militants, but was generally restrained in his reaction and never threatened military retaliation. The two countries have resumed periodic "trust-building" talks between foreign ministers and foreign secretaries in recent months.
Mr Obama praised the relationship between the US and India as one of the "defining partnerships of the 21st century". He and Mr Singh said they would co-host an international education summit next year and said the US Department of Homeland Security and India's Ministry of Home Affairs would collaborate to combat terrorism by improving security at airports and seaports.
The leaders also reaffirmed their pledges of newfound economic co-operation, including moves by the United States to ease export controls affecting trade between the world's two largest democracies. Speaking to the sensitivity about high unemployment in the US, Mr Singh said at one point that his country "is not in the business of stealing jobs from America".
The US leader's final day in India began with a grand welcome ceremony at Rashtrapati Bhavan, the palatial residence of India's president. Later, Mr Obama and First Lady Michelle Obama placed a wreath at Raj Ghat, a memorial to Mohandas Gandhi. As a sign of respect, the Obamas removed their shoes before placing a large white wreath on a flower-covered tablet in front of an eternal flame.