Singh said he was also confident Obama would "operationalise the nuclear deal as early as possible".
"There are a few 'i's and 't's that have to be crossed, but I am confident and I have the assurance that that process can be completed without much further loss of time."
Later on Tuesday Obama hosted what the White House said was his first state banquet, in honour of the Indian prime minister.
The black-tie party on the South Lawn was attended by 300 guests, featuring a mostly vegetarian meal of curry prawns, aged basmati rice, eggplant salad, lentil soup, potato dumplings and other delicacies.
Earlier the two men also addressed regional security.
Obama would not reveal whether he intended to increase US troop levels in Afghanistan, saying his intention was to "finish the job", but that the Afghan people would "ultimately have to provide for their own security".
"The changes that have come over in India are simply phenomenal ... in economic and military terms, it is a formidable power"
Robert Wirsing, Professor of International Studies at Georgetown University
He said that he would announce his strategy for Afghanistan after the Thanksgiving holiday has ended at the weekend.
Referring to the Mumbai attacks in India last year, the president said: "It is in our strategic interests, in our national security interest, to make sure that al-Qaeda and its extremist allies cannot operate effectively.
"We are going to dismantle and degrade their capabilities and ultimately dismantle and destroy their networks."
His comments came just hours after Singh urged Washington to stop "premature talks of exit from Afghanistan" that would "only embolden the terrorist elements who are out to destabilise ... the civilised world".
But while Obama said the US would continue to pressure Pakistan to "use all its influence to curb the power of the terrorist groups" within the country, he acknowledged Washington needed to provide support to civilians and civil society, and not just the Pakistani military.
New Delhi has blamed a Pakistan-based group for last year's attack on Mumbai, which left more than 160 people dead.
Singh also said the two countries were planning new agreements on the development and sharing of renewable energy technology.
Obama confirmed the initiative, announcing a greater number of scientific exchange programmes for agricultural, medicinal and environmental studies, saying the two countries had moved closer to a "strong operational agreement" on climate change at next month's Copenhagen summit.
"It's essential that countries do what is necessary to reach a strong operational agreement."
Though both leaders stuck to issues on which both sides shared the same views, analysts said the tone struck before and during the talks suggests a much closer relationship than ever before.
The Indian prime minister had already told the Council on Foreign Relations in Washington of a new partnership that would contribute to "an orderly transition to the new order and be an important factor for global peace and stability".
Speaking to Al Jazeera on Tuesday, Robert Wirsing, a professor of international relations at Georgetown University, said the state visit marked a new era in relations between the world's largest democracies.
"The fact is that India is playing an increasingly important role in the international economy. The changes that have come over in India are simply phenomenal ... in economic and military terms, it is a formidable power.
"American investment opportunities are huge ... India is talking about spending $150 billion in its nuclear industry ... and of course India is the largest importer of weapons in the world ... it was these issues that dominated the talks."