"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.
At an emergency meeting, Olmert told members of his ruling party on Wednesday that he plans to stay on to shepherd through recommendations proposed by the government panel on the war, his spokesman said.
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.
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.
Since the report was issued, Olmert has been scrambling to hold his coalition together. One minister from the Labor Party, the junior coalition partner, already has quit, and there have been increasing signs of eroding support within Kadima.
In a new blow to Olmert, the chairman of Kadima's parliamentary faction, Avigdor Yitzhaki, resigned and called for the prime minister to do likewise.
"In order for Kadima to return to being a legitimate ruling party and for the sake of the prime minister and for the sake of the entire country, I think the prime minister has to resign," he told Israel Radio. "He has to take this responsibility and resign."
The war broke out last July 12 after Hezbollah guerrillas crossed into Israel, killed three soldiers and captured two others. Olmert's public support, high in the early days of the war, nose-dived after the fighting ended without Israel's achieving the two goals Olmert declared — crushing Hezbollah and recovering the captured soldiers.
On Thursday, Olmert's opponents from all sides planned a show of strength at a demonstration in downtown Tel Aviv. Its size and composition could go a long way toward showing Olmert whether he can weather the storm.
On May 28, the Labor Party, Olmert's main coalition partner, holds a primary election where Peretz, also a target of criticism from the inquiry commission, is likely to be replaced.
Two of the four candidates opposing Peretz have called on Olmert to resign, and Labor could well leave his coalition, probably forcing elections.