In order to meet climate goals, Rishi Sunak has pledged not to "unnecessarily" raise costs or "burden" households.
According to the prime minister, he is still committed to reaching net zero by 2050, but any new initiatives must be "proportionate and pragmatic.".
His lawmakers are calling for a revision of his green policies.
It follows an unexpected victory for the Tories in a by-election in which they ran a campaign opposed to the expansion of London's clean-air zone.
The Conservative candidate in Uxbridge and South Ruislip opposed Sadiq Khan's plan to expand the Ultra Low Emission Zone (Ulez), which imposes a daily fee on drivers of more polluting vehicles.
Labour, which had been predicted to win the seat in outer London, blamed Ulez for its loss and said it might now want to reconsider its expansion strategy.
Discussions about the price and timing of carbon emission reduction measures have been reignited as a result.
Former business secretary Sir Jacob Rees-Mogg has urged the government to reconsider new rules for energy certificates and drop plans to outlaw the sale of new gasoline and diesel vehicles in 2030.
He stated on Sunday that "the lesson from Uxbridge is that there are things we can change that will be electorally successful.".
Right-wing Tory MP Danny Kruger, who is the co-leader of a new group, made a similar call for a "rethink about the pace and the mechanism of the change we all want to see" over the weekend.
He said on BBC Radio 4's Westminster Hour, "We need a transition that is affordable, and particularly affordable for working families.
When asked whether he would buck backbench pressure on the matter from his MPs, Mr. Sunak responded that, in an era of rising living expenses, he was "standing up for the British people.".
Bills for households and families are being affected by that, and he continued, "I don't want to do anything to add to that; I want to make it easier.".
"We're going to move closer to net zero, but we're going to do it in a reasonable, practical way that doesn't needlessly add stress or expense to people's lives. ".
The remarks follow recent suggestions from other ministers that some green policies should be approached differently.
The government should extend a deadline for landlords to meet new energy efficiency goals, according to Housing Secretary Michael Gove, who also said that ministers were "asking too much too quickly.".
Mark Harper, the transport secretary, announced earlier this month that he had stopped the government from funding low-traffic neighborhoods and urged local councils to take another look at unpopular areas in their communities.
According to a report in The Times, ministers are thinking about denying councils access to the national database of license plates that is used to enforce the schemes.
The newspaper also claimed that smaller automakers would be given more time to transition to electric vehicles if there was an "Aston Martin exemption" to the 2030 car sales deadline.
Lord Zac Goldsmith, who resigned from his position as a Foreign Office Minister last month and criticized the PM's "apathy" regarding climate change, recently questioned Mr. Sunak's dedication to green policies.
Speaking to reporters on Monday, Mr. Sunak stated that he found it "important" to achieve net zero, which would mean stopping the production of new greenhouse gases into the atmosphere.
It was "better than the vast majority of other countries that we're compared to," he continued, adding that the UK should be proud of its track record in this regard.
The Uxbridge by-election, according to Lisa Nandy, shadow secretary for communities, "sent a very clear message" to Labour that the cost of living was "really biting for people.".
She continued by stating that since plans like Ulez were created, pressures on living expenses had "worsened" and that "we will respond to that, and we will reflect on that.".
The speaker continued, "We're absolutely committed to cleaning up our air, but we've got to make sure we do this in a way that is helpful, and affordable for people who are currently in really tough situations.
