"For the first time in history, all major economies have come together to accept their responsibility to take action to confront the threat of climate change.
"This progress did not come easily and we know this progress alone is not enough ... We've come a long way but we have much further to go."
Obama said the US, China, Brazil, India and South Africa had agreed to limit global warming to two degrees Celsius to help meet their new objective.
The deal calls for the participating countries to list specific actions they have taken to control emissions and their commitments to achieve deeper reductions.
The agreement also includes a commitment by the countries to give developing nations $100bn dollars in assistance from 2020 to help them deal with climate change.
The deal includes some progress in helping developing nations cope with climate change, but it falls short of committing any nation to pollution reductions.
But many countries are angry they were excluded from the negotiations and are debating whether or not to approve the deal.
They also criticised the agreement because it was non-binding and set no overall target for curbing greenhouse gas emissions.
"You are going to endorse this coup d'etat against the United Nations," Claudia Salerno Caldera, Venezuela's representative, told Lars Loekke Rasmussen, the Danish prime minister and the conference chairman, in a speech from the floor.
"Those of us who wish to speak have to make a point of order by cutting our hands and drawing blood," she said, opening a red-stained palm.
Opposition to deal
Tuvalu's Ian Fry, whose country is one of the most at risk from global warming, said the deal amounted to a betrayal.
"It looks like we are being offered 30 pieces of silver to betray our people and our future," he said.
"There were too many nationalist self-interests to set aside ... What we got was completely watered-down from what even the most optimistic person would have hoped at the beginning of these discussions 12 days ago"
Alan Fisher, Al Jazeera's correspondent at the summit
"Our future is not for sale. I regret to inform you that Tuvalu cannot accept this document."
For any deal to become a UN pact it would need to be adopted unanimously at the 193-nation talks.
Some European leaders have accepted the deal, but Jose Manuel Barroso, the European Commission president, said that it was "clearly below" the goal of the European Union.
"I will not hide my disappointment," he said.
Al Jazeera's Alan Fisher, reporting from the Danish capital, said there were "too many obstacles to overcome" for world leaders to reach a more significant breakthrough.
"There were too many nationalist self-interests to set aside," he said.
"What we got was completely watered-down from what even the most optimistic person would have hoped at the beginning of these discussions 12 days ago.
"There is some anger among [many] ... developing nations. They say that this deal has been done essentially with the Americans, the Chinese, the South Africans and the Brazilians and the Indians and they have had no real input.
"They're concerned that ... this agreement has been taken forward, when there has been no real wider discussion."
Earlier on Friday, world leaders had appeared to mount a last-minute bid to save the pact, but these efforts only achieved agreement on a consensus-driven deal with few specifics that many admitted would fall short of what was needed.
|Obama acknowledged that the deal did not go far enough to address climate change [EPA]
The tense haggling capped two years of deadlock over crafting a new UN treaty from 2013 that would reduce global warming from mortal threat to manageable peril.
But sideline negotiations have revealed deep divisions between rich and poor, entrenched in a textual battlefield over how to curb carbon emissions and muster funds to fight climate change.
Manmohan Singh, the Indian prime minister, acknowledged the outcome "may well fall short of our expectations" but called for follow-up negotiations to be completed by the end of 2010.
Yukio Hatoyama, the Japanese premier, who has offered nearly $20bn towards a global climate fund, said the summit would deliver a "robust" if "not necessarily perfect" statement on fighting global warming.
But Dmitry Medvedev, the Russian president, said the world community had "clearly underestimated" the task of reaching not just a binding agreement but even a general declaration.
"We still have long and difficult road ahead of us," he said.
Hugo Chavez, Venezuela's president, was bluntest: "The meeting has not been a success - it has failed."
One member of the Maldives delegation, the Indian Ocean archipelago which fears being swallowed up by rising sea levels in a matter of decades, added: "Whatever the outcome, it looks bad for us."