The commission's report focuses on the first five days of Israeli military action following the capture of two Israeli soldiers by Hezbollah fighters in June last year.
Ofir Pines, a former Labour cabinet minister, said both Olmert and Amir Peretz, the defence minister, should stand down.
"I expect the prime minister and the defence minister to stand up and take responsibility and resign," he told Army Radio.
Gideon Saar, a senior member of the main opposition party, Likud, said: "He has to accept responsibility. The people deserve better."
Staying put
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"A former cabinet minister said both Olmert and Amir Peretz, the defence minister, should resign"
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Another Labour politician, Danny Yatom, said the entire cabinet should resign, since they unanimously approved the decision to go to war.
"The whole cabinet is party to these matters," he told Israel Radio.
"They are all partners ... by virtue of their vote, and by the fact that they didn't stand up and say a word even if they had something to say."
Lieutenant-General Dan Halutz has already resigned in the face of public criticism of his handling of the conflict.
Olmert was quoted by the YNet news website as telling members of his cabinet at their weekly meeting: "We cannot talk about what has been leaked. We will wait for the report, read it, study it and then we'll respond."
Olmert's aides have said he has no intention of resigning.
The prime minister has argued that Israel made strategic gains in the war in a ceasefire deal that left Hezbollah not in control of some of its territory under a strengthened UN peacekeeping force.
Popularity drop
Hezbollah fired about 4,000 rockets into Israel during the war, sending a million people into shelters in attacks the Israeli military failed to stop.
Olmert's approval rating has since plunged to single digits in opinion polls.
Suzanne Peretz, a spokeswoman for Kiryat Shmona, a northern Israeli town hit by Hezbollah fire, said: "There was no prime minister. There was no government. We were screaming for help."
Al Jazeera's Jacky Rowland in Jerusalem says the report is likely to damage Olmert's standing further.
"One newspaper said his standing was somewhere between critical and terminal."
The report's harshest criticism is reserved for Halutz, who has already resigned, Rowland said.
At least 1,200 Lebanese, including an estimated 270 Hezbollah fighters, and 117 Israeli soldiers and 41 civilians were killed in the conflict.