Mr Brown said ministers faced an "uphill struggle" but that he was determined to play his part in "bringing the world together".
He told BBC One's Breakfast programme: "If you don't get an agreement this week, people will doubt whether you can get an agreement at all."
He said negotiations were so complex because of the number of countries involved but that there was "goodwill".
"If we make promises at Copenhagen, we've got to be sure that every country is going to keep them."
Environment ministers and negotiators from 193 countries are taking part in discussions, with 120 national leaders joining on Thursday with the aim of signing a deal the following day.
Mr Brown said: "We can't do it on our own, it's about the whole world coming together.
"I want every country and not just a few countries to sign the deal. It's about... each doing something to help climate change.
"Unless we have a solution we're going to have [our children] growing up in a world where there are floods and droughts, where there are climate change refugees and evacuees, where we have extreme weather."
The prime minister is putting his weight behind a private carbon market, allowing countries and businesses to buy and sell emissions allowances, as a way of encouraging them to cut carbon output.
However, BBC environment analyst Roger Harrabin said this was a controversial viewpoint.
"A lot of people are saying carbon markets don't work. They provide a lot of money for investment... but they are inherently risky," he said.
The majority of the world's governments believe carbon emissions are contributing to climate change but developing countries staged a walkout earlier this week, claiming richer nations were trying to dodge their obligations.
The UK is backing new plans by Ethiopian prime minister Meles Zenawi to raise $50bn (£31bn) per year for African nations by 2015. The BBC understands this could involve international taxes on financial transactions, aviation and shipping fuel.
Conservative leader David Cameron said people must change the way they lived to help achieve an 80% cut in carbon emissions by 2050 and that it was right for the UK to provide £1.5bn to help developing countries.
"It's in our interests that we deal with this," he told BBC Radio 5 live.
"If we don't do something about this, we will have climate change refugees... because you will see the deserts expanding, the glaciers drying up, large parts of the world without drinking water.
"A lot of those people will arrive on our doorstep, so it's not some far off problem that will only affect other people."
He said it was important not to "depress ourselves" because "a lot of things we can do will be good for our economy, cut our bills, make life better to live".
On Tuesday, the Prince of Wales warned delegates the "eyes of the world" were upon them and said they had the power to "write our future".
He said the planet had reached a "point of crisis" and urged leaders to "listen to the cries" of those already suffering from climate change.
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