"I told him that resignation would be the right thing for him to do," said Foreign Minister Tzipi Livni, the most popular politician in Olmert's Kadima Party and the best placed to succeed him as party leader — and possibly as prime minister.
Livni is the most senior official to join a flood of calls for Olmert's resignation, reports CBS News correspondent Robert Berger.
In other developments:
Livni said she would remain in government "to ensure that improvements are carried out." Livni, Olmert's top rival in the party, said she believed Kadima could replace Olmert without holding new elections.
Under Israel's parliamentary system, Kadima could change leaders without losing power. Livni said when Kadima holds its party primary, she would run for the leadership. No primary date has been set.
"It's not a personal matter between me and the prime minister — this issue is more important than both of us," Livni said.
Olmert called an emergency meeting of his Cabinet Wednesday in a feverish attempt to hold on to power, urging his rivals to "slow down" before trying to reap political capital from a scathing report on his handling of last year's war against Hezbollah guerrillas in Lebanon.
This week's report has fueled a growing chorus of calls for Olmert's resignation, including from members of his coalition government.
The 34-day war has been widely perceived as a failure. Monday's report said Olmert bore ultimate responsibility, accusing him of poor judgment, hasty decision making and lack of vision.
A defiant Olmert opened the special Cabinet session by hinting that reports of his political demise were premature. "To those who are eager to take advantage of this report to reap certain political advantages, I suggest 'slow down,'" he said in comments broadcast on Israeli media.
Israel Radio has reported that Defense Minister Amir Peretz, also the target of fierce criticism over Israel's prosecution of the Lebanon war, may decide to resign his post as early as Wednesday.
Two new polls published in Israeli newspapers Wednesday said some two-thirds of Israelis want Olmert to resign immediately. The surveys indicated that the hawkish former prime minister, Benjamin Netanyahu of the opposition Likud Party, would likely win handily if new elections were held.