David Cameron is being pressed to adopt tougher targets to deal with climate change, the BBC has learned.
David Cameron has led calls for a climate change bill
Both Mr Cameron and the government are calling for a cut of 60% in carbon emissions by 2050.
But the Quality of Life policy group, set up last year by Mr Cameron, says this target lacks "credibility" and it should in fact be 80%.
The group is also critical of a key part of the Stern Report into the costs of global warming.
The Treasury-commissioned Stern report, published earlier this month, warns of the financial catastrophe facing the world if climate change is not tackled.
Conservative MP Nick Hurd, author of the Tory policy group report, said Stern's view on the sort of cuts in carbon emissions required to prevent disaster were too optimistic.
He said Stern had "value in pointing out to us that the costs of inaction far outweigh the costs of action".
But he added: "Where we are disappointed is that he is danger of teeing us up with an insurance policy that will not cover the risk."
He was particularly critical of Stern's view on stabilising carbon emissions at about 3C above the levels found in the atmosphere before widespread industrialization, arguing it should be much lower than that.
"We need to be much more ambitious in reducing global temperatures to no more than 2C above pre-industrial levels.
"At the moment the language is all about 60% cuts. We are working on the basis that it should be 80%," said Mr Hurd.
He also wants to see a binding target to cut emissions by 2025, proposed by an independent agency and supported by a Commons vote.
Mr Cameron set up the Quality of Life policy group last year, under chairman John Gummer and deputy chairman Zac Goldsmith, to come up with policy ideas for the next Tory election manifesto.
Mr Hurd said the policy group's aim was to see "how we can decarbonise the British economy by 2050 without sacrificing quality of life and the competitiveness of the British economy".
Mr Cameron, who has led calls for a climate change bill, has said carbon should be cut "at least 60%" by 2050.
He has also called for binding annual targets for cuts in emissions, although a memo leaked last week to the Labour party suggests this idea could be dropped.
Commenting on Mr Hurd's report, Shadow Environment Secretary Peter Ainsworth said: "The Quality of Life Policy Group has produced a thoughtful and challenging report which is a timely reminder of the dangers of complacency."
The government has announced plans for a climate change bill, which would make its long-term goal of a 60% reduction in carbon dioxide emissions by 2050 a legally binding target.
The bill, outlined in the Queen's Speech, will also establish a "Carbon Committee" to ensure the target is met.
But it makes no reference to annual CO2 reductions targets.