Mr Sharif has staked his name on restoring the judges to their jobs
Nine ministers from a leading party in Pakistan's new coalition have handed in their resignations, plunging the country into political uncertainty.
Ex-PM Nawaz Sharif decided to pull his PML-N out of government because it had failed to meet a promise to reinstate judges sacked by President Musharraf.
The resignations, which the prime minister has yet to accept, follow landmark general elections in February.
Coalition leaders deny the six-week-old government is in danger of collapse.
But analysts have called the pull-out a huge set-back that could lead to growing instability.
The BBC's Barbara Plett in Islamabad says the move has raised fears of another round of political turbulence in Pakistan.
She says further cracks in the alliance may give a lease of life to pro-Musharraf parties which were defeated in recent elections.
Prime Minister Yousuf Raza Gilani is waiting until Mr Zardari returns from abroad before accepting the resignations, an aide said.
Mr Sharif and his main coalition partner, Pakistan People's Party leader Asif Zardari, say they will continue working together while trying to resolve differences over how to reinstate deposed judges.
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The judges' issue should be put on back burner and other issues like state of economy and energy crisis should be addressed.
Our correspondent says Mr Sharif lost patience after a second deadline was missed on Monday.
He has said his party will continue to support the government on an issue-by-issue basis.
"We will not become part of any conspiracy to destabilise the democratic process," he said on Monday.
But Mr Sharif also said his party would join lawyers in protest, demanding that the government reinstate the judges.
Our correspondent says the restoration of the judges is opposed by President Musharraf who sees them as hostile to his rule.
Analysts say he would welcome a split in the coalition, which has sidelined him since winning elections in February.
A split would also reinforce a perception that Mr Zardari is working with the unpopular president.
Reinstating the judges was one of Mr Sharif's key election promises and his condition for joining the coalition.
March 2007: President Musharraf suspends Supreme Court chief justice, triggering protests
6 Oct 2007: President Musharraf wins election
3 Nov 2007: President declares state of emergency and sacks around 60 judges
22 Nov 2007: New Supreme Court upholds Musharraf election win
18 Feb 2008: New coalition government of PPP and PML-N emerge victorious in parliamentary polls
30 April 2008: Deadline set by two parties to reinstate sacked judges
12 May 2008: Second deadline to restore judges
He wants the judges to be given their jobs back without conditions.
Mr Zardari says their reinstatement should be part of a larger package of constitutional amendments which would include reducing their powers.
President Musharraf sacked about 60 judges - some sitting in the Supreme Court - in November 2007, after declaring a state of emergency.
The Supreme Court had been due to rule on whether his re-election was legal.
It had also been due to rule on a controversial amnesty covering Mr Zardari and his wife Benazir Bhutto, who was later assassinated.
Analysts say the coalition parties are deeply politically divided - the Pakistan People's Party wanted to avoid a confrontation with the president, while Nawaz Sharif was prepared for one.