Gordon Brown said negotiators had 50 days to save the world from global warming and break the "impasse".
He told the Major Economies Forum in London, which brings together 17 of the world's biggest greenhouse gas-emitting countries, there was "no plan B".
World delegations meet in Copenhagen in December for talks on a new treaty.
'Rising wave'
The United Nations (UN) summit will aim to establish a deal to replace the 1997 Kyoto treaty as its targets for reducing emissions only apply to a small number of countries and expire in 2012.
Mr Brown warned that negotiators were not reaching agreement quickly enough and said it was a "profound moment" for the world involving "momentous choice".
"In Britain we face the prospect of more frequent droughts and a rising wave of floods," he told delegates.
"The extraordinary summer heatwave of 2003 in Europe resulted in over 35,000 extra deaths.
Grim warning
"On current trends, such an event could become quite routine in Britain in just a few decades' time. And within the lifetime of our children and grandchildren the intense temperatures of 2003 could become the average temperature experienced throughout much of Europe."
The costs of failing to tackle the issue would be greater than the impact of both world wars and the Great Depression combined, the prime minister said.
The world would face more conflict fuelled by climate-induced migration if a deal was not agreed, he added.
He told the forum, on the second day of talks in the capital, that by 2080 an extra 1.8 billion people - a quarter of the world's current population - could lack sufficient water.
Mr Brown said: "If we do not reach a deal at this time, let us be in no doubt: once the damage from unchecked emissions growth is done, no retrospective global agreement, in some future period, can undo that choice.
"So we should never allow ourselves to lose sight of the catastrophe we face if present warming trends continue."
Agreement at Copenhagen "is possible", he concluded.
"But we must frankly face the plain fact that our negotiators are not getting to agreement quickly enough. So I believe that leaders must engage directly to break the impasse."
In recent days there have been a number of warnings that progress is stalling.
Rajendra Pachauri, head of the Intergovernmental Panel on Climate Change, told Newsweek magazine "the prospects that states will actually agree to anything in Copenhagen are starting to look worse and worse".
The Major Economies Forum is not part of the formal UN process and so firm commitments are unlikely to come from the meeting.
It is seen instead as a gathering where countries can explore options and positions in a less pressured environment.
He told the Major Economies Forum in London, which brings together 17 of the world's biggest greenhouse gas-emitting countries, there was "no plan B".
World delegations meet in Copenhagen in December for talks on a new treaty.
'Rising wave'
The United Nations (UN) summit will aim to establish a deal to replace the 1997 Kyoto treaty as its targets for reducing emissions only apply to a small number of countries and expire in 2012.
"In Britain we face the prospect of more frequent droughts and a rising wave of floods," he told delegates.
"The extraordinary summer heatwave of 2003 in Europe resulted in over 35,000 extra deaths.
Grim warning
"On current trends, such an event could become quite routine in Britain in just a few decades' time. And within the lifetime of our children and grandchildren the intense temperatures of 2003 could become the average temperature experienced throughout much of Europe."
The costs of failing to tackle the issue would be greater than the impact of both world wars and the Great Depression combined, the prime minister said.
The world would face more conflict fuelled by climate-induced migration if a deal was not agreed, he added.
He told the forum, on the second day of talks in the capital, that by 2080 an extra 1.8 billion people - a quarter of the world's current population - could lack sufficient water.
Mr Brown said: "If we do not reach a deal at this time, let us be in no doubt: once the damage from unchecked emissions growth is done, no retrospective global agreement, in some future period, can undo that choice.
"So we should never allow ourselves to lose sight of the catastrophe we face if present warming trends continue."
Agreement at Copenhagen "is possible", he concluded.
"But we must frankly face the plain fact that our negotiators are not getting to agreement quickly enough. So I believe that leaders must engage directly to break the impasse."
In recent days there have been a number of warnings that progress is stalling.
Rajendra Pachauri, head of the Intergovernmental Panel on Climate Change, told Newsweek magazine "the prospects that states will actually agree to anything in Copenhagen are starting to look worse and worse".
The Major Economies Forum is not part of the formal UN process and so firm commitments are unlikely to come from the meeting.
It is seen instead as a gathering where countries can explore options and positions in a less pressured environment.