The Israeli cabinet is holding an extraordinary session to discuss its response to a damning report on the handling of the 2006 Lebanon conflict.
Ehud Olmert is under mounting pressure over the war
One cabinet minister has quit after the study accused Prime Minister Ehud Olmert of judgement errors and there are calls for Mr Olmert to follow suit.
Avigdor Yitzhaki, the chairman and co-founder of Mr Olmert's Kadima party, is among those demanding he resign.
But Mr Olmert is resisting, cautioning against a hasty response to the report.
"To all those who are in haste in order to take advantage of the report for political profit, I tell them not to be hasty," Mr Olmert warned at the start of the emergency meeting.
Mr Yitzhaki told Israel Radio the prime minister had to go so Kadima "can continue with his mandate".
According to the Israeli daily Haaretz, Mr Yitzhaki has said he will resign himself if Mr Olmert does not step down in the course of the day.
Defence Minister Amir Peretz, who was also severely criticised by the report, is considering stepping down, Israel Army Radio says.
Aides close to Mr Peretz were quoted as saying that he is thinking about resigning and could do so "within hours".
Newspaper polls published on Wednesday suggest that the vast majority of Israelis want Mr Olmert to leave office.
A poll in the mass circulation Yediot Aharonot had 65% of Israelis questioned wanting Mr Olmert out, compared with just 10% who thought he should stay.
A survey in the left-of-centre Haaretz daily had 68% calling for his resignation and 40% backing early parliamentary elections.
A poll published in the Maariv daily put the percentage of people wanting Mr Olmert to quit even higher, at 73%.
The six-month government probe, led by retired judge Eliahu Winograd, accused Mr Olmert of "serious failure in exercising judgement, responsibility and prudence" during the war against Hezbollah.
It also accused Defence Minister Amir Peretz and then chief of staff General Dan Halutz of serious failures, but stopped short of calling for any resignations.
Speaking on Wednesday, Mr Yitzhaki said that since there are no elections in sight Mr Olmert must step aside: "The Kadima party must choose its chief for the three years that remain for the (current) legislature."
"A leader can only lead a public where he has, firstly, legitimacy and its confidence. The prime minister should act responsibly and resign to allow a new coalition to be formed by Kadima."
On Tuesday cabinet minister Eitan Cabel, a member of the Labour Party, the main partner in the ruling coalition with Mr Olmert's Kadima party, became the first member of the Mr Olmert's government to resign over the report.
"I cannot sit in a government headed by Ehud Olmert," Mr Cabel said, calling for Mr Olmert to resign immediately.
Mr Cabel, who did not hold a portfolio, said Mr Olmert should resign as he had "lost the trust of the people" following the investigation.
Mr Olmert is already suffering unprecedented unpopularity levels for an Israeli prime minister and is expected to face calls for his resignation at a mass rally planned for Thursday in Tel Aviv.
About 1,200 Lebanese and 160 Israelis were killed after Israel launched a 34-day war against Hezbollah militants who had captured two Israeli soldiers.
The two soldiers remain in captivity.