Gordon Brown said that he would like a global movement similar to the Make Poverty History campaign to persuade leaders to reach agreement.
Mr Brown’s comments came at the Labour Party conference, where he shared a platform with Spain’s centre-left Prime Minister Jose Luis Zapatero and his Norwegian counterpart Jens Stoltenberg.
He added that richer nations would have to help pay for poorer countries to develop clean energy sources.
Mr Brown proposed a $100bn fund paid for by wealthy countries to help achieve the target of reducing carbon emissions.
He told delegrates: "Like Jens and Jose Luis, I think we can, even though it is difficult, reach a climate change agreement in December."
Mr Brown said there had been progress in Japan, China and in the USA, where President Barack Obama was "utterly committed" to reaching a deal.
He added: "We know that people are prepared to accept a 50% cut by 2050 in addition to an 80% cut by developed countries.
"We know also that people are prepared to accept that we have got to work together and finance what we do for developing countries if we are going to get an agreement."
Before the summit there had to be an agreement on intermediate targets and nations had to show their commitments could be delivered.
Turning to finance, Mr Brown said: "We are putting forward an idea that I think will gain support for $100bn to be that the richest countries pay to the poorest countries to ensure that they can make the climate change changes that they need to do by 2020."
Mr Brown said a political deal would happen only "if we can mobilise public opinion, not just in our country but right across the world.
He added: "just like Make Poverty History mobilised millions of people right across the continents of the world, so I believe that the desire for an agreement at Copenhagen can mobilise millions of people too."
"I believe that is going to be a vital factor in persuading world leaders that they must not only come to the table but come to an agreement in Copenhagen."
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