A few hours later however, Israel's Channel 2 reported that a majority of parliamentarians from Olmert's Kadima party now believed that he should step down as leader.
The channel also said that Kadima's MPs would press Olmert to step down as party leader at a meeting expected to be held on Thursday, when parliament meets to debate Eliyah Winograd's interim report on the war.
Separately, Channel 10 reported that Tzipi Livni, the foreign minister, had told her aides that Olmert "must go." Lizni is a favourite to succeed Olmert as the leader of Kadima.
Eitan Cabel, an entrepreneur and businessman, played little role in the 2006 war and has for several months hinted that he was considering leaving politics, Israeli media has reported.
Cabel's resignation follows increasing speculation in Israeli media that Olmert and Amir Peretz, the country's defence minister, would soon resign in response to popular discontent over their handling of the war in Lebanon in summer 2006.
"A former cabinet minister said both Olmert and Amir Peretz, the defence minister, should resign"
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A poll on Tuesday conducted by public radio found that 69 per cent of the Israeli public think the prime minister should resign and 74 per cent believe Peretz, who is also the chairman of the Labor party, should also step down.
The government commission, appointed by Olmert seven months ago, accused him of "serious failure in exercising judgement, responsibility and prudence" during last year's war against Hezbollah.
The report was equally withering about Peretz and Dan Halutz, the then chief of staff, concluding that they had failed in fulfilling their functions.