Theresa May has said "it can't be right for Big Ben to be silent for four years" after parliamentary officials announced plans to silence its bongs.
The chimes are being stopped to allow extensive renovation work to the Elizabeth Tower, the Great Clock and its bell.
But the Prime Minister called on Commons Speaker John Bercow to "urgently" review the plans.
During a visit to Portsmouth, she told reporters: "Of course we want to ensure people's safety at work but it can't be right for Big Ben to be silent for four years.
"And I hope that the Speaker, as the chairman of the House of Commons commission, will look into this urgently so that we can ensure that we can continue to hear Big Ben through those four years."
Mrs May waded into the row after returning to the UK following a walking holiday in Switzerland.
Brexit Secretary David Davis said stopping the chimes was "mad" as he dismissed health and safety concerns linked to the clock tower's restoration and urged the estate's authorities to "just get on with it".
The move was also labelled "entirely bonkers" by Conservative MP James Gray who sat on the administration committee which first approved the work.
Parliamentary officials defended the plan, insisting workers' hearing would be put at "serious risk" and warned that those using the 100 metre high scaffolding around the tower could also be startled by the 118 decibel bongs.
And 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.
But MPs have asked officials to look at the cost and practical implications of ringing the Great Bell more often than the current plan to put it back into use for special occasions, such as New Year's Eve.
Liberal Democrat Tom Brake has contacted Ian Ailles, House of Commons director general, calling for the review of the plans to be carried out.
Mr Brake, who answers questions from MPs on behalf of the Commons Commission, said: "I have asked whether someone can do some work working out what the costings and the practicality of ringing them more frequently would be.
"It would not be possible for them to continue to be rung every 15 minutes as is currently the case, that would not be practical, but it may be perhaps practical and it may be financially viable to ring them more frequently than is currently being proposed."
MPs did not know about the four-year silence when the plans were signed off, he said.
It will be the longest period Big Ben has been silenced in its 157-year history and will begin after noon on Monday August 21.
The £29 million renovation includes the installation of a lift and repairs to the clock's hands, mechanism and pendulum.
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.