Ehud Barak, also the leader of the country's Labor party and Olmert's main coalition partner, called a news conference in response to damaging testimony given in the corruption probe against Olmert Tuesday.
"I don't think the prime minister can at the same time lead the government and handle his own affairs," Barak said. "The prime minister needs to disconnect himself from the day to day management of the government."
In Tuesday's testimony by a U.S. businessman, Olmert was accused of using donations to fund his lavish lifestyle.
If Barak and his Labor party withdraw from the current coalition government, Olmert would no longer have a parliamentary majority and new elections would have to be held. A primary election is not due until 2010.
Israel's foreign minister, Tzipi Livni, would become interim prime minister if Olmert steps down.
Olmert has denied all wrongdoing and has said all donations were used for legitimate campaigning. He did not issue any immediate response to Barak, but earlier Wednesday an aid said the prime minister "doesn't have any intention to resign or to step down temporarily, even if Barak asks him to," reported the Associated Press.
However, Olmert has promised to resign if he is indicted.
Yuval Steinitz, a member of the hard-line opposition Likud party, criticized Barak for not setting a firm deadline and calling for immediate elections.
The corruption investigation against Olmert centers on tens of thousands of dollars in donations he collected before becoming prime minister in 2006.
Prosecutors suspect him of accepting bribes and violating campaign-finance laws.
Tuesday's testimony came from key witness Morris Talansky, who claims he gave Olmert $150,000 over 15 years, often in cash, and was asked to pay for everything from expensive cigars to an Italian vacation.
Talansky said he did not expect anything in return for the money, but overlooked many inappropriate requests for cash and personal expenses.
"The relationship of 15 years was purely of admiration," Talansky said, reported ABC news. "I never expected anything personally. I never had any personal benefits from this relationship whatsoever."
Olmert was a powerful political figure before becoming prime minister. He served as mayor of Jerusalem for 10 years beginning in 1993. He was then named minister of industry and trade.
Public opinion of Olmert has dipped with the latest allegations, and he has struggled to win back popular support since Israel's inconclusive war against Hezbollah in Lebanon in 2006.
