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Insulate Britain has announced it will "suspend its campaign of civil resistance" until 25 October, in an open letter written to Prime Minister Boris Johnson.
The campaign group has been causing chaos by blocking major roads around London.
Police have made multiple arrests during the demonstrations, with angry motorists often clashing with protesters.
Several injunctions against the protesters granted by the High Court in recent weeks means anyone breaching the order by blocking roads could face a prison sentence, Transport Secretary Grant Shapps has said.
The environmental group said in its open letter on Thursday: "Insulate Britain would like to take this opportunity to profoundly acknowledge the disruption caused over the past five weeks.
"We cannot imagine undertaking such acts in normal circumstances. But the dire reality of our situation has to be faced.
"We invite you to make a meaningful statement that we can trust… that your government will take the lead needed to insulate and retrofit our homes."
"Ahead of COP26, Insulate Britain will suspend its campaign of civil resistance until Monday 25th October," the letter added.
A member of the Insulate Britain group tried to give their letter to the police guards at the gate of Downing Street to pass to Mr Johnson.
The officers refused, stating they do not take letters on behalf of the prime minister.
The group then vowed to return to protesting in the roads if Mr Johnson does not meet its demands to deliver "a meaningful or trustworthy statement" over improving the insulation in British homes.
It wants the government to insulate all UK homes by 2030 to cut carbon emissions.
Biff Whipster, a retail worker from Canterbury who attempted to hand the letter in on Thursday, said: "We want to now give the government a bit of breathing space so they don't feel under pressure.
"They can re-read what their own advisers have been telling them, read the science and basically come up with what's the best business case for Britain, which is to insulate our homes, create proper jobs, and reduce CO2 emissions.
He added: "Let's have a 10-day pause and we will continue if there is not a meaningful statement or trustworthy statement from Mr Johnson about what actions he's taking."
Mr Whipster also said he had resigned himself to the possibility of potentially being thrown in prison or breaking court injunctions with his continued protesting.
"Then we will recommence blocking roads, blocking motorways and breaking court injunctions."
The group has blocked roads on 14 days over the past five weeks, with activists often gluing their hands to the carriageway to increase the length of time it takes for police to remove them.