Kadima deputies declared Olmert the victor in the showdown with Livni after hours of intense debate.
"It would be best if he resigned and if the country elects a candidate who would reach for peaceful solutions"
Casey, Kitchener, Canada
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"The parliamentary bloc stands behind the government and the prime minister," they said in a statement.
Shimon Peres, the deputy prime minister, said after the 29-strong parliamentary caucus that "the prime minister enjoyed unprecedented support".
Livni, a 48-year-old rising star and deputy leader of Kadima, could be fired from Olmert's cabinet.
Israeli media quoted aides as saying the prime minister may dismiss her and fight to stay on, despite opinion polls showing two-thirds of Israelis think he should go and mounting pressure within his own party.
Avigdor Yitzhaki, Kadima's parliamentary leader, resigned and called on Olmert to "act responsibly and resign".
Under Kadima's rules, Olmert cannot be ousted. The only course of action is to persuade him to resign, officials say.
Parliament, which will hold a debate on Thursday on the commission's findings, could force him out through a no-confidence vote but there does not yet appear to be a majority to do so.
Kadima's main coalition partners, notably the Labour party, have so far stuck by Olmert, apparently keen to avoid an early election that could end up reducing their parliamentary power.
An Olmert loyalist was named to replace Yitzhaki, Israeli media reported.
The government-appointed Winograd commission said Olmert had "made up his mind hastily" to launch the campaign against Hezbollah in July and accused him of "a serious failure in exercising judgment, responsibility and prudence".
His declared aims in going to war, to free two soldiers seized by Hezbollah and crush the armed group, were "overly ambitious and impossible to achieve", the commission said in its report on the 34-day conflict.
At an emergency cabinet meeting earlier on Wednesday, Olmert acknowledged personal failings.
|"I suggest that all those who are in a hurry to take advantage of this report and make political gain - slow down"|
Ehud Olmert, Israeli prime minister
He said: "It is primarily incumbent on this government, which is responsible for the failings, to also be responsible for fixing them.
"I suggest that all those who are in a hurry to take advantage of this report and make political gain - slow down."
Dan Halutz, former Israeli military chief, stepped down earlier this year, and aides to Amir Peretz, Israel's defence minister, told Israel Radio and Army Radio he was considering stepping down.
Opinion polls in three major Israeli newspapers showed 65 to 73 per cent of the public wanted Olmert to quit.
The two frontrunners to replace Olmert are Livni, and Benjamin Netanyahu, the former prime minister and Likud party chairman.