The Just Stop Oil group has suspended its disruptive protests until Monday, April 25.
The eco campaigners said they want to give Prime Minister Boris Johnson the opportunity to issue a statement agreeing to their demands.
Protesters began their action on April 1, blocking key oil terminals such as the Buncefield terminal in Hemel Hempstead, Hertfordshire, and the Navigator Thames terminal in Essex.
The protests led to dry petrol pumps in parts of the East of England, including Cambridgeshire, Suffolk and Norfolk.
A Just Stop Oil letter to Boris Johnson reads: "Recent polling and the actions taken since April 1 by the Just Stop Oil coalition have demonstrated that the vast majority of the country back the coalition demand that there should be no new oil and gas.
"It is supported by scientists, academics, your own Climate Change Committee and the International Energy Agency."
It adds: "Your government has admitted this will do nothing to help ordinary people pay their bills.
"The policies that would help people now - support for home insulation and onshore wind - have been axed.
"While ordinary people struggle with the cost of living crisis driven by high oil and gas prices, the profits and the share price of BP and Shell continue to rise.
"The Just Stop Oil coalition has taken the decision to suspend activities until the April 25 to give you the opportunity to make a statement on behalf of the government that it will immediately halt all future licensing and consents for the exploration, development and production of fossil fuels in the UK."
Downing Street has previously criticised the "guerrilla tactics" of the environmental protest group.
On April 11, a spokesperson for the Conservative government said: "We recognise the strength of feeling and the right to protest is a cornerstone of our democracy.
"But we won’t tolerate guerrilla tactics that obstruct people going about their day-to-day business."
The Labour Party has criticised protesters and called for the government to apply for injunctions to stop the protests.
"Motorists were already being hammered by prices at the pump, and now millions can’t even access fuel," a Labour spokesperson said.
On April 13, during a visit to Hertfordshire, Liberal Democrat leader Sir Ed Davey told the Local Democracy Reporting Service: "The police were right to make those arrests.
"This is an unlawful protest, and the police have our full support to deal with these protesters."
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