The call came as COP26 UK president Alok Sharma warned “we still have a mountain to climb” for the United Nations climate change conference to reach a successful conclusion.
Mr Brown, the World Health Organisation's ambassador for global health finance, said there were still several days left to “turn around” the gloomy assessment in a leaked official communique he said had expressed “deep concern” the funding target had not been achieved.
He said: "If we don’t reach the target we have set of a $100bn a year in climate finance for developing countries, we will deprive them of the opportunity, not only to build coastal defences and renewable industries, but to build the healthcare systems that are necessary for resistance to droughts and famine, and pollution in the air.
"We need a global burden-sharing agreement over the longer term, and that is not forthcoming at the moment.
"In the short term, we need at least to meet the commitments we have made 11 years ago to provide $100bn a year, and haven't done so.
"It is vital now, in the next few days, that the Prime Minister and the Chancellor, finance ministers maybe meeting virtually, make a final push to get to this $100bn – and hopefully get more.”
Speaking at a panel debate on Tuesday at the conference on “action now for climate and health”, Mr Brown said a leaked COP26 communique had expressed “deep concern” at the failure to get to $100bn.
But he said: "Surely we can turn that round.
“We have a few days to do this.
"The future of healthcare systems depends on it, but also the future of the other climate activity that is being promoted here this week.”
Mr Brown warned the Glasgow conference risked being compared to a previous UN COP conference in the Danish capital 12 years ago, which was widely regarded as unsuccessful.
He said: "We do not want Glasgow to be like Copenhagen in 2009 – fail.
"We want Glasgow to be like Paris – and indeed better than Paris – in 2015, and succeed.
"In the next few days, I plead with our world leaders to get together and make good the promises that are essential for a world that is going to be habitable in the future.”
He told UK Foreign Office minister Wendy Morton, who was chairing the panel discussion: “I would urge you to bring together ministers in all the different countries, even at this late stage, because if we go away from Glasgow without having achieved one of the main objectives, people will say that we have not done enough and we have let future generations down – and young people will not forgive us.”
Mr Brown underlined the key importance of such “global burden sharing”, where richer countries responsible for the largest emissions historically “make good” the necessary funding for mitigation and adaptation measures against climate change in poorer nations, including their health systems.
He said: "You cannot solve the problem of our health crisis without solving climate change, and you cannot solve the problem of climate change without building resilient healthcare systems, because alone they emit 4-5 per cent of carbon emissions throughout the world.”
Hours later, Mr Sharma said: “The time has now come to find political consensus on the areas of divergence.
“We have only a few days left.
"We are making progress at COP26, but we still have a mountain to climb over the next few days.
"What has been collectively committed to goes some way, but certainly not all the way, to keeping 1.5C [global temperature rise] within reach.
"The gap in ambition has narrowed.
“Now the world needs confidence that we will shift immediately into implementation, that the pledges made here will be delivered, and that the policies and investment will swiftly follow.
"We have an opportunity to succeed."
Mr Sharma said there was now an “urgency” to the negotiations and said the deadline for agreement was 6pm on Friday.
He said: "There has been some progress, but quite clearly not enough.
"I genuinely think this is ‘all hands on deck’.
"I know the negotiators have been working literally night and day on this.
"There is a sense of urgency and I would very much like us to finish at the time that has been set out.
"There has been a constructive spirit among negotiators and I hope that will produce the result we want.”