He added that the offer was on the table "if -- and only if -- it is part of the broader accord" including transparency.
The White House had hoped for an agreement before the president's high-stakes visit, but negotiations had been doomed to failure even before the conference began. In Copenhagen, negotiators worked through the night and met for hours behind closed doors in the hopes of reaching some sort of an agreement, with U.S. officials working quickly to reach a compromise before Obama's arrival.
In the last-minute push, even Secretary of State Hillary Clinton made an unscheduled appearance to urge on her international counterparts.
China has been hesitant to commit to a deal where it would be open to scrutiny by the international community. Leaders from the country have balked at measures to allow international monitors to verify emissions cuts that might be agreed to in the deal.
In the last 24 hours, officials say China had softened its opposition to verification of emissions reductions. Clinton announced Thursday that the United States will contribute to a $100 billion fund by 2020 to help poor countries cope with climate change, but that financial help is conditional on China relenting on verification, a move that could exert pressure on China.
But China and the United States still appear to be divided on the issue of verification.
The notion that the success of the climate agreements may hinge on the United States and China has frustrated leaders of some developing countries.
Speaking as the voice of the developing world, Brazilian President Lula da Silva gave a passionate speech where he scolded the developed world for not negotiating on climate change in good faith with poorer nations. He also said this conference is not about climate change, but about economic opportunities for the developing world.
With an array of challenges the president has to confront at home -- from health care to unemployment to the economy -- the president is putting his prestige at stake, both at home and abroad, to fly to Copenhagen and seal a deal on an issue that lacks the support of China, one of the biggest polluters in the world.
The U.S. president usually goes on trips like this when an agreement has already been worked out, but the White House says it is not a surprise that Obama went. His job as a leader, sources say, is to lead and that's what he wants to do in Copenhagen.
Obama's schedule is fluid at this point. The president was scheduled to meet with Rasmussen first thing upon arrival in Copenhagen before the climate change summit sessions, but instead, he went straight to a multilateral meeting, which included leaders from the European Union, India, Russia and Brazil.
When asked how long Obama will stay if there is no deal, a White House official said the "intention" is for the president to be Copenhagen only today.
Obama, whose Nobel Peace Prize win was partially attributed to his efforts on climate change, does not only face the skepticism of an international audience, but even his supporters back home. If he didn't go to Copenhagen, he would upset his liberal base.
It remains unclear where there will be a legally binding international treaty reducing greenhouse gas emissions worldwide, as had been the original goal of the conference. What leaders are hoping at this point is to have a more informal agreement that can be built upon down the road.