Theresa May says it "can't be right" for Big Ben to be silenced for four years during renovation work, calling on the Speaker of the House to "urgently" review the plans.
The House of Commons Commission will now consider how long the bongs should be halted for following concerns raised by a number of MPs.
When they signed the plans off, MPs did not know about the four-year silence.
It would be the longest period Big Ben has been silenced in its 157-year history and is set to begin after noon on Monday August 21.
The 13.7-tonne Great Bell was last stopped for maintenance in 2007 and before that was halted for two years in 1983 for refurbishment, but has been stopped on a number of other occasions since it first sounded in 1859.
The £29 million renovation includes the installation of a lift and repairs to the clock's hands, mechanism and pendulum.
Parliamentary officials defended the plan to silence the bongs, insisting workers' hearing would be put at "serious" risk, and warning that those using scaffolding around the tower could be startled by the noise, placing them in danger.
They dismissed suggestions the chimes could be restored during the hours that work is not being carried out as the process takes about half a day to complete.
The prime minister has joined fellow Conservative politicians in calling for the plans to be reconsidered.
Brexit Secretary David Davis said stopping the chimes was "mad" as he dismissed health and safety concerns linked to the clock tower's restoration.
The move was also labelled "entirely bonkers" by Conservative MP James Gray who sat on the administration committee which first approved the work.
But Labour leader Jeremy Corbyn has told LBC the safety of those working on the clock tower is paramount.
"It's not a national disaster or catastrophe" if Big Ben has to be silenced for a while, he said.