Britain's leading scientists have challenged the US oil company ExxonMobil to stop funding groups that attempt to undermine the scientific consensus on climate change.

In an unprecedented step, the Royal Society, Britain's premier scientific academy, has written to the oil giant to demand that the company withdraws support for dozens of groups that have "misrepresented the science of climate change by outright denial of the evidence".

The scientists also strongly criticise the company's public statements on global warming, which they describe as "inaccurate and misleading".

In a letter earlier this month to Esso, the UK arm of ExxonMobil, the Royal Society cites its own survey which found that ExxonMobil last year distributed $2.9m to 39 groups that the society says misrepresent the science of climate change.

These include the International Policy Network, a thinktank with its HQ in London, and the George C Marshall Institute, which is based in Washington DC. In 2004, the institute jointly published a report with the UK group the Scientific Alliance which claimed that global temperature rises were not related to rising carbon dioxide levels in the atmosphere.

"There is not a robust scientific basis for drawing definitive and objective conclusions about the effect of human influence on future climate," it said.

In the letter, Bob Ward of the Royal Society writes: "At our meeting in July ... you indicated that ExxonMobil would not be providing any further funding to these organisations. I would be grateful if you could let me know when ExxonMobil plans to carry out this pledge."

The letter, a copy of which has been obtained by the Guardian, adds: "I would be grateful if you could let me know which organisations in the UK and other European countries have been receiving funding so that I can work out which of these have been similarly providing inaccurate and misleading information to the public."

This is the first time the society has written to a company to challenge its activities. The move reflects mounting concern about the activities of lobby groups that try to undermine the overwhelming scientific evidence that emissions are linked to climate change.

The groups, such as the US Competitive Enterprise Institute (CEI), whose senior figures have described global warming as a myth, are expected to launch a renewed campaign ahead of a major new climate change report. The CEI responded to the recent release of Al Gore's climate change film, An Inconvenient Truth, with adverts that welcomed increased carbon dioxide pollution.

The latest report from the UN Intergovernmental Panel on Climate Change (IPCC), due to be published in February, is expected to say that climate change could drive the Earth's temperatures higher than previously predicted.

Mr Ward said: "It is now more crucial than ever that we have a debate which is properly informed by the science. For people to be still producing information that misleads people about climate change is unhelpful. The next IPCC report should give people the final push that they need to take action and we can't have people trying to undermine it."

The Royal Society letter also takes issue with ExxonMobil's own presentation of climate science. It strongly criticises the company's "corporate citizenship reports", which claim that "gaps in the scientific basis" make it very difficult to blame climate change on human activity. The letter says: "These statements are not consistent with the scientific literature. It is very difficult to reconcile the misrepresentations of climate change science in these documents with ExxonMobil's claim to be an industry leader."

Environmentalists regard ExxonMobil as one of the least progressive oil companies because, unlike competitors such as BP and Shell, it has not invested heavily in alternative energy sources.

ExxonMobil said: "We can confirm that recently we received a letter from the Royal Society on the topic of climate change. Amongst other topics our Tomorrow's Energy and Corporate Citizenship reports explain our views openly and honestly on climate change. We would refute any suggestion that our reports are inaccurate or misleading." A spokesman added that ExxonMobil stopped funding the Competitive Enterprise Institute this year.

Recent research has made scientists more confident that recent warming is man-made, a finding endorsed by scientific academies across the world, including in the US, China and Brazil.

The Royal Society's move emerged as Chris Rapley, director of the British Antarctic Survey, warned that the polar ice caps were breaking up at a faster rate than glaciologists thought possible, with profound consequences for global sea levels. Professor Rapley said the change was almost certainly down to global warming. "It's like opening a window and seeing what's going on and the message is that it's worse than we thought," he said.