The UK's energy and climate change secretary has insisted the last-minute agreement at the Copenhagen summit is "not the final word" on the issue.
Delegates largely backed a US-led deal which includes limiting temperature rises to less than 2C.
Ed Miliband said it was significant as it marked a sense that both developed and developing countries wanted to tackle the problem.
Gordon Brown earlier pledged to push for a legally binding treaty.
On Saturday morning delegates recognised the agreement that the US reached with key nations including China and Brazil.
The UN Secretary General Ban Ki-moon said the agreement must be made legally binding next year.
Earlier, the meeting failed to secure unanimous support, amid opposition from some developing nations.
I am now going to lead a campaign around the world with other countries for the legally binding treaty that is the obvious next stage from this
Mr Miliband said: "It's not the final word at all, it's the end of the beginning. It marks a real sense that developed and developing countries, despite their constraints, want to tackle the problem.
"What is different about this agreement is not just the developed world, but India and China, and all the other countries of the developing world have committed to hard targets."
But he said he had wanted a stronger outcome than the US-led agreement, which would recognise a temperature increase limit of 2C (3.6F) and put aside $100bn to help poorer countries cope.
"I don't think it's the full agreement we would have wanted. We would have wanted a clearer tract to a legally binding treaty, we would have wanted legally binding targets, ideally. We'd have wanted more clarity of ambition for 2050," he said.
The former deputy prime minister, John Prescott - who helped negotiate the Kyoto Protocol that set emissions targets in 1997 - denied the talks in Copenhagen had failed.
He said the problem was that the accord had been presented as if "America had done a deal".
"That causes quite a lot of resentment," he said. "The developing countries think they've perhaps been fobbed off with money.
"But at the end of the day we have now the first stage of the second stage agreement which now goes to the protocols."
It is not even an agreement. The parties rejected it as being a consensus decision
Tom Picken, Friends of the Earth
But Liberal Democrat energy spokesman Simon Hughes said the declaration was "desperately disappointing" when the world needed a deal.
He said: "I can't remember an occasion when more people of power and influence came together on a more important issue and went away with so little to show for it."
Shadow climate change secretary Greg Clark said talks must go on in the months ahead until a proper deal is struck.
He said: "I made it clear in Copenhagen that, if negotiations continue beyond the general election and Conservatives were in government, there would be no let up in our determination to secure a rigorous global deal."
Green Party leader Caroline Lucas said the outcome after years of waiting was "a complete disaster".
She said: "What have we got? An empty accord with no legally binding framework, no targets, and no money guaranteed to be over and above existing aid budgets. It's deeply, deeply disappointing."
Friends of the Earth campaigner Tom Picken said the UK government had said it would fight for a "strong and fair agreement" but the accord was neither.
"It is not even an agreement," he said. "The parties rejected it as being a consensus decision."
He accused the US of "arm twisting" some countries into a deal and said the rich countries had acted against the spirit of the past two years of negotiations.
As details emerged of the agreement, the prime minister said there had been progress, although he added that "it is not enough" and he wants "to go further quickly".
Mr Brown said: "I am now going to lead a campaign around the world with other countries for the legally binding treaty that is the obvious next stage from this.
Gordon Brown says he will lead a campaign for a legally binding treaty on climate change
"We've got, for the first time, agreement about the limits to which we can allow emissions to go."
The prime minister said he expected all countries to agree to the 2C limit for 2050.
Mr Brown also said every country would now be expected to produce a national emissions plan that would be open to "international scrutiny".
"It is the first time anything global like this has been agreed. Kyoto was not global - it was only a number of countries that signed up," said the prime minister.
He said once countries publish their plans in the coming weeks it would become clear that "it is a major number of gigatonnes that are being reduced in carbon emissions".
Former government chief scientific adviser, Sir David King, said the summit had come one year too early for Mr Obama to be able to take leadership of the issue.
"He's in a hostage position in relation to his own Senate. He has to wait until next March when his Senate has declared what the United States can do before he can take an internationally leading position," he said.
"I see momentum has gathered, I see the big step forward is a range of nations committing themselves to a reduction in carbon dioxide emissions."
Lord Smith, chairman of the Environment Agency, said it was a "disappointing" outcome because so few countries were involved in the final accord.
"I think we always knew that we weren't going to emerge from Copenhagen with a completely legally binding signed and sealed treaty, but I think we'd hoped for something rather better than this," he said.
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