Mr Olmert has previously said he will not step down
Israeli Defence Minister Ehud Barak has called on Prime Minister Ehud Olmert to take a leave of absence or resign as he battles allegations of corruption.
Mr Barak said he would take his Labour Party out of Mr Olmert's governing coalition if he did not step down.
"The prime minister needs to disconnect himself from the day-to-day management of the government," Mr Barak said.
Mr Olmert denies claims that he took up to $500,000 (£250,000) in bribes or illegal campaign donations.
Mr Olmert, the head of the Kadima party, admits accepting funds before he became prime minister in 2006.
But he insists they were legal contributions towards his campaigns for re-election as Jerusalem mayor and for the leadership of the Likud party.
He has previously said he had no plans to step aside unless he is charged.
Kadima has just 29 MPs out of a total of 120 seats in the Knesset, and relies on the Labour Party's 19 MPs as key allies in its governing coalition.
Mr Barak's resignation call is a very damaging blow to Mr Olmert, the BBC's Tim Franks in Jerusalem says.
Most seasoned political analysts in Israel believe it spells his certain demise as prime minister, our Middle East correspondent says.
Mr Barak was speaking a day after the US businessman at the centre of the allegations told investigators that he gave Mr Olmert envelopes full of cash.
Kadima: 29 MPs
Labour: 19 MPs
Shas: 12 MPs
Likud: 12 MPs
Yisrael Beiteinu: 11 MPs
Others: 37 MPs
Morris Talansky was questioned by investigators, and is due to be cross-examined by Mr Olmert's defence team in July.
At a press conference on Wednesday, Mr Barak said he did not think the prime minister could run the government and deal with the fall-out from the allegations at the same time.
"He can do this in any of the ways open to him - suspension, vacation or resignation or declaring himself incapacitated. We will not be the ones to determine this," he said.
But he warned that if Mr Olmert did not leave, "we will act towards setting an agreed and early date for elections".
However, our correspondent notes that Mr Barak did not issue an ultimatum with a precise deadline attached.
Testifying in an Israeli court on Tuesday, Mr Talansky said he handed over about $150,000 of his own money to Mr Olmert, directly and through aides, over a 15-year period.
The rest of the money came from fundraising.
Mr Talansky said the money was often handed over in cash-stuffed envelopes
He said he did not know how the money had been spent, adding: "I only know he loved expensive cigars. I know he loved pens, watches."
Mr Talansky said that Mr Olmert also asked him for a personal loan of $25,000-$30,000 for a holiday in Italy.
In another case, he said, he walked to a bank to withdraw $15,000 in cash for a loan as Mr Olmert waited in a luxury hotel.
Mr Talansky said he thought Mr Olmert's "word was gold", but that Mr Olmert never repaid either loan.