The emissions cuts offered so far at the Copenhagen climate change summit would still lead to global temperatures rising by an average of 3C, according to a confidential UN analysis obtained by the Guardian.

With the talks entering the final 24 hours on a knife-edge, the emergence of the document seriously undermines the statements by governments that they are aiming to limit emissions to a level ensuring no more than a 2C temperature rise over the next century, and indicates that the last day of negotiations will be extremely challenging.

A rise of 3C would mean up to 170 million more people suffering severe coastal floods and 550 million more at risk of hunger, according to the Stern economic review of climate change for the UK government – as well as leaving up to 50% of species facing extinction. Even a rise of 2C would lead to a sharp decline in tropical crop yields, more flooding and droughts.

Tonight hopes of the summit producing a deal were rising after the US, the world's biggest historical polluter, moved to save the talks from collapse.

The secretary of state, Hillary Clinton, committed the US to backing a $100bn-a-year global climate fund from 2020 to shield poor countries from the ravages of global warming. Barack Obama is expected to offer even more cash when he flies in tomorrow.

Another key obstacle – the fate of the Kyoto treaty – was solved, with China and the developing world seeing off attempts to kill the protocol. But the UN analysis suggests much deeper cuts will have to be agreed tomorrow to achieve the stated objective of limiting temperature rises to 2C.

The document was drafted by the UN secretariat running the Copenhagen summit and is dated 11pm on Tuesday night. It is marked "do not distribute" and "initial draft". It shows a gap of up to 4.2 gigatonnes of carbon emissions between the present pledges and the required 2020 level of 44Gt, which is required to stay below a 2C rise. No higher offers have since been made.

"Unless the remaining gap of around 1.9-4.2Gt is closed and Annexe 1 parties [rich countries] commit themselves to strong action before and after 2020, global emissions will remain on an unsustainable pathway that could lead to concentrations equal or above 550 parts per million, with the related temperature rise around 3C," it says. It does not specify a time when 3C would be reached but it is likely to be 2050.

Greenpeace campaigner Joss Garman said: "This is an explosive document that shows the numbers on the table at the moment would lead to nothing less than climate breakdown and an extraordinarily dangerous situation for humanity.

The UN is admitting in private that the pledges made by world leaders would lead to a 3C rise in temperatures. The science shows that could lead to the collapse of the Amazon rainforest, crippling water shortages across South America and Australia and the near-extinction of tropical coral reefs, and that's just the start of it."

Bill McKibben, founder of the campaign 350.org, said: "In one sense this is no secret – we've been saying it for months. But it is powerful to have the UN confirming its own insincerity." He did not know why his name was written on the top of the document.

However, Bob Ward, at the Grantham Research Institute on Climate Change at the London School of Economics, said current ambitions could still be consistent with a 50% chance of meeting the 2C target. "But it would require steeper reductions after 2020, which are likely to be more costly, to be well below 35 billion tonnes in 2030 and well below 20 billion tonnes in 2050."

The goal of keeping the increase in global average temperatures below 2C, relative to pre-industrial levels, has become the figure that all rich countries have committed to try to achieve in Copenhagen. However, 102 of the world's poorest countries are holding out for emission cuts resulting in a temperature increase of no more than 1.5C.

Failing to do that, they say, would leave billions of people in the world homeless, facing famine and open to catastrophic weather-related disasters. But such an ambitious target would mean carbon would have to be removed from the atmosphere.

The internal paper says: "Further steps are possible and necessary to fill the gap. This could be done by increasing the aggregated emission reductions [in rich countries] to at least 30% below the baseline levels, further stronger voluntary actions by developing countries [such as China and India] to reduce their emissions by at least 20% below business as usual, and reducing further emissions from deforestation and international aviation and marine shipping."

Oxfam International's climate adviser, Hugh Cole, said: "At this stage, a deal that fails to keep temperature rises below two degrees is simply not good enough."

Earlier this week Rajendra Pachauri, who heads the UN's Intergovernmental Panel on Climate Change, said that even with 1.5C rises, many communities would suffer.

"Some of the most vulnerable regions in the world will be worst affected. These will be the largest countries in the developing world. They have little infrastructure that might protect them from climate change. The tragedyof the situation is that those countries that have not at all contributed to the problem of climate change will be the ones most affected," he said.

"Some parts of the world, which even with a 1.5C rise, will suffer great hardship and lose their ability to lead a decent and stable form of existence. If we are going to be concerned about these communities, then maybe 1.5C is what we should be targeting. But if we can find means by which those communities can be helped to withstand the impact of climate change with substantial flow of finances, then maybe one can go to 2C."

A UK government spokesman said last night: "The UK government continues to work towards a 2 degree deal at Copenhagen and current ambitions set us on track to meet that target. We know however that more needs to be done before the talks conclude and that's why the Prime Minister, the Climate Change Secretary and British negotiators will be working over these crucial next hours to secure a deal that delivers."