BP and Shell are being told to tear up their membership of the American Petroleum Institute (API) in protest at the organisation's attempts to incite a public backlash against Barack Obama's energy and climate change bill.

The two oil companies are also being asked to bring a halt to their own political lobbying in Washington in letters sent to their chief executives from Greenpeace and the Platform environmental group.

"BP maintains its membership of the API through paying substantial fees based on the large size of BP's business. It is our concern that these fees are used by the API to undermine US government action on climate change and that BP's membership of the API contradicts its position on the issue," writes John Sauven, executive director of Greenpeace UK, in a letter to Tony Hayward, the BP boss.

The letter also questions the $8m (£4.8m) worth of spending on lobbying in Washington since the start of 2009, saying this runs against the commitment made by BP's former boss, Lord Browne, in 2002 that BP would from now on "make no political contributions from corporate funds anywhere else in the world". A similar letter has been sent to Peter Voser, the new boss at Shell.

The demands from Greenpeace follow revelations in the Guardian last Friday that the API was pumping money into a series of "citizen rallies" to put pressure on the Obama administration over its support for a climate change bill sponsored by Congressmen Henry Waxman and Edward Markey which comes before the Senate next month.

The proposed legislation, which has already successfully passed through the House of Representatives, marks a clear move by the US to adopt a greener political and economic agenda and ditch the kind of sceptical views on global warming that were the hallmark of the previous government run by George W Bush, himself a former oilman.

An email sent by Jack Gerard, president of the API, says the lobby group will provide "upfront resources" to pay for a highly experienced events company to organise the public protest meetings, but it says oil companies themselves should encourage their staff to go to some of the 20 rallies being considered.

"In the 11 states with an [oil] industry core, our member company local leadership – including your facility manager's commitment to provide significant attendance – is essential," the note says.

Greenpeace and Platform believe these actions are "astroturfing" – a determined attempt to create a false appearance of popular opposition to the Obama plans to control carbon emissions from oil while boosting wind and other cleaner technologies. The environmentalists remind Hayward and Voser that their companies were once members of the API-backed Global Climate Coalition in the US which successfully campaigned against it signing the Kyoto protocol on the grounds that there was not enough proof that global warming was being made worse by man-made carbon dioxide pollution.

After protests, BP and later Shell withdrew from the GCC and started to make tentative investments in renewable energy, notably wind farms in America, which continue today. The two companies are now actively involved in the United States Climate Action Partnership, which is seen by environmentalist campaigners to be playing a very positive role on driving forward the green agenda in a country only recently overtaken by China as the world's biggest carbon producer.

BP said it was "highly unlikely" it would pull out of the API, which was just one of hundreds of trade bodies to which it was affiliated. But it stressed that it was not involved directly in any of the planned public rallies. "Our views on climate change legislation are fairly well known," said a BP spokesman at its London headquarters. "We support action to counter emissions although we favour market mechanisms, like trading schemes."

Shell said tonight that it had told the API that it would not participate in the rallies but indicated it would not be leaving the organisation. "Our focus is on seeking common ground with stakeholders that can aid Congress in enacting a fair and effective cap and trade program. We will continue to express our position within API and other business and trade associations of which we are members," added a spokesman at its headquarters in The Hague.

Meanwhile ExxonMobil, a stalwart of previous opposition to Kyoto but a company that insists it is not a climate change denier, seems to support the API wholeheartedly. The part of the company's website devoted to the "ExxonMobil Citizen Action Team" gives pride of place to an official letter from the API opposing the Waxman-Markey legislation.

A note above from Rex Tillerson, chairman and chief executive of the world's biggest publicly quoted oil company, says: "Our elected officials make decisions that affect all of us. It is critical that we as a company, and more importantly as individuals, are part of the political process. By linking ExxonMobil employees and retirees to their elected officials, we can let our representatives know that the ExxonMobil family is an important force in civic life."