About 100 leaders attended the talks, ahead of the Copenhagen summit which is due to approve a new treaty.
At the close of the meeting, Mr Ban said: "While the summit is not the guarantee that we will get the global agreement, we are certainly one step closer to that global goal today."
He praised world leaders for their desire to tackle climate change.
"Climate change is a defining challenge of our time, he said.
"Today's summit signals a determination of world leaders to address this challenge and reach a substantive deal in Copenhagen."
Negotiators for the Copenhagen summit are trying to agree on a replacement for the Kyoto Protocol to limit carbon emissions.
The Chinese president said his country would curb its carbon emissions per unit of Gross Domestic Product by a "notable margin" by 2020 from the 2005 level.
Hu Jintao: Developed nations need to do more
However, the proposal is unlikely to mean an overall reduction in emissions, as China's economy is expected to continue to grow rapidly.
A US official said that China's proposals were helpful but Beijing needed to provide figures.
"It depends on what the number is," US President Barack Obama's climate change envoy Todd Stern said, quoted by Reuters news agency.
But Mr Gore praised China's "impressive leadership".
"We've had... indications that in the event there is dramatic progress in this negotiation, that China will be prepared to do even more," he said.
BBC environment reporter Matt McGrath says that much of the debate about tackling global warming revolves around the idea of absolute cuts in emissions of carbon dioxide - but developing countries like India and China feel that this emphasis is unfair.
Richer countries, meanwhile, have had the benefits of centuries of fossil fuel use, and are now demanding that growing nations stop using them with no obvious alternatives in place, he says.
Mr Hu also pledged to "vigorously develop" renewable and nuclear energy.
He restated China's position that developed nations needed to do more than developing nations to fight climate change because they were historically responsible for the problem.
"Developed countries should fulfil the task of emission reduction set in the Kyoto Protocol, continue to undertake substantial mid-term quantified emission reduction targets and support developing countries in countering climate change," he said.
In other speeches at the summit:
US President Obama acknowledged that the US had been slow to act, but promised a "new era" of promoting clean energy and reducing carbon pollution
The new Japanese Prime Minister, Yukio Hatoyama, pledged to reduce emissions by 25% by 2020 compared to the 1990 level, calling it the Hatoyama Initiative
French President Nicolas Sarkozy called on leaders to meet again in mid-November ahead of the crucial Copenhagen conference
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