Theresa May is facing calls from Britain’s leading environment and development groups to use her influence to persuade Donald Trump that the US must remain committed to the Paris climate change agreement.

In a strongly worded letter, the heads of Oxfam, the RSPB, Greenpeace, WWF, Christian Aid, Cafod and other groups have called on the prime minister to “pick up the phone” to the US president to warn him of the consequences of leaving the Paris accord, something Trump pledged to do within 100 days of coming to power, a timeline that passed last week.

The UK played a leading role in the complex negotiations that resulted in nearly 200 nations making the unprecedented commitment to tackle global climate change, signed in Paris in December 2015.

The agreement is seen as crucial for the success of efforts to limit the global temperature rise to below 2C above pre-industrial levels by 2100. But reports in the US suggest that support for leaving the climate treaty is gaining ground among Trump’s key advisers as the president – who has said climate change is a Chinese hoax – prepares to deliver his decision, which is expected this week.

The reported shift in opinion among White House aides comes despite strong calls from leading businesses and scientists for the US to remain in the climate accord. Last week, major US companies including Google, Microsoft and Walmart wrote to Trump stating the economic and business case for the US continuing to be a party to the agreement.

May herself recently came under pressure from cross-party MPs and leading scientists who urged her to use her influence to persuade the US president to acknowledge and act on climate change.

A recent ComRes survey showed almost two-thirds of British adults (64%) accept that climate change is happening, and that it is primarily due to human activity.

The joint letter warns May that Trump “may be about to undermine a vital global agreement on which the health, security, and prosperity of hundreds of millions of people depend”.

It continues: “This climate agreement was an extraordinary feat of international diplomacy, and the UK played a crucial role in securing it. This is now the best chance humanity has to avert full-blown climate change, and may well be the last. A strong majority of people in the UK believe climate change is happening. They will be looking to you as the prime minister to champion science, moral responsibility and international cooperation.”

In recent days European ministers and EU officials have been lobbying senior White House staff after hearing Trump was leaning heavily towards leaving the accord.

The UN environment chief, Erik Solheim, has also warned the US that it will “shoot itself in the foot” if it quits the Paris deal because China, India and Europe will snap up the best power sector jobs in future.

“There is no doubt where the future is and that is what all the private sector companies have understood,” Solheim told Reuters. “The future is green. Obviously if you are not a party to the Paris agreement, you will lose out. And the main losers will be the people of the United States itself because all the interesting, fascinating new green jobs would go to China and to the other parts of the world that are investing heavily in this.”

An online petition launched by Greenpeace calling on May to intervene had reached 78,000 signatories by Saturday evening.