JERUSALEM — Prime Minister Olmert decided yesterday not to sack his foreign minister, Tzipi Livni, even though last week she called on him to resign for his mishandling of last year’s war in Lebanon.

Mr. Olmert took the view that sacking her would create unnecessary turmoil at a time when he remains politically weak, and so, in a remarkable display of accommodating a political foe, he resolved to carry on working with Ms. Livni.

His decision reflected the desire of most members of the government to avoid going to the country at all costs. Polls suggest Mr. Olmert’s Kadima-led government would lose by a landslide if a general election were called soon.

Ms. Livni is left politically weakened after being forced to work alongside Mr. Olmert just days after she publicly withdrew her backing for him.

The pair met briefly after yesterday ‘s Cabinet meeting in Jerusalem and issued a statement saying they “agreed to work together in the government led by Ehud Olmert.”

Pursued by local reporters, Ms. Livni later added that she wanted to put personal issues behind her so she can focus on foreign policy. “All I am interested in are the diplomatic issues on the agenda,” she said. “Foreign relations are not a personal issue.”

Her comments betrayed none of the high politics that the pair were caught up in last week, with Ms. Livni reckoning that Mr. Olmert had no option other than to resign following the publication of the preliminary findings of the Winograd inquiry into Israel’s management of the war.

This led to Mr. Olmert’s advisers and allies turning on Ms. Livni, briefing against her in the Israeli media, accusing her of cowardice and, over the weekend, suggesting that she lied to the inquiry about her own role in the war.

Although she is weakened after yesterday’s decision, Ms. Livni’s call for her boss to go could boost her profile in the long term.

Those who want to stop her taking over from Mr. Olmert at a later date have even begun discussing promoting Shimon Peres, the veteran politician who left Labor for Kadima, into the top job if Mr. Olmert is forced to stand down.

While Mr. Olmert has surprised many observers by holding on to his office following the Winograd inquiry, he is still vulnerable on several fronts.

First, the inquiry will publish its full findings this summer and could even call for him to stand down.

A second and more pressing concern for Mr. Olmert is next week’s leadership election in the Labor Party, one of the key coalition partners in his government.

If a leader is elected who decides to pull Labor’s 19 MPs out of the ruling coalition, then it will fall.