JERUSALEM — Prime Minister Olmert yesterday lost the backing of both his foreign minister and the parliamentary coalition leader over his mishandling of the war in Lebanon.

A former member of Mossad, Tzipi Livni spent 90 minutes in private conversation with Mr. Olmert before emerging to tell a press conference that she had urged her boss to resign.

“I told him that resignation would be the right thing for him to do,” the foreign minister and deputy prime minister said.

Her decision to effectively drop Mr. Olmert was seen as a gambit to put herself in poll position to replace him.

If successful, it would make the 48-year-old mother-of-two Israel’s first female prime minister since Golda Meir held the post in the 1970s.

Mrs. Livni is the daughter of an underground fighter who battled for Israel’s independence in the 1940s.

She has quickly risen through the ranks of Israeli politics in recent years and appears to be the Kadima Party’s best hope of retaining power.

Mrs. Livni said that although she did not fully support Mr. Olmert as prime minister, she would continue to work for him.

The fact that he did not immediately sack her for disloyalty showed the weakness of his current political position.

“I haven’t worked and am not working to topple the prime minister,” she said.

“That’s a decision he’ll have to make.

“It’s not a personal matter between me and the prime minister — this issue is more important than both of us.”

Mr. Olmert was also abandoned by another key former ally, Avigdor Itzhaki.

Mr. Itzhaki stood down as the parliamentary head of Kadima, the party Mr. Olmert led to victory in the general election in March 2006.

Mr. Itzhaki, a founder member of Kadima — which is the senior partner in the five-party coalition government — said he felt it would be “suicide” for Mr. Olmert to carry on.

Currently raising just 2% support in public opinion polls, Mr. Olmert’s political plight looks increasingly desperate.

But the nature of coalition politics in Israel means his career will not be over until the other four parties in the coalition decide it would be better to vote against him.

The fact that these parties face crushing defeat at the next general election means it is possible his coalition could limp on for another few months.

The present crisis was prompted by Monday’s publication of the preliminary findings of the Winograd committee of inquiry into last summer’s war between Israel and Hezbollah in Lebanon.

The preliminary findings said Mr. Olmert had not listened to advice and rushed into a war that Israel effectively lost.

His supporters likely will try to argue that he should not go until the final report is published later this year, possibly as soon as late July.

But a large anti-Olmert demonstration due to take place in Tel Aviv Thursday could force his hand.

The rally will be the clearest proof of how the public regard Mr. Olmert, and if the tens of thousands protesters promised by the organizers materialize, then it may well mark the beginning of the end of his political career.