"I can no longer sit in a government led by Ehud Olmert," said Cabel, the first member of Olmert's government to resign over the Winograd Commission report on the war's handling which was released on Monday.
"A former cabinet minister said both Olmert and Amir Peretz, the defence minister, should resign"
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Following Cabel's announcement at a news conference, the prime minister's office immediately said that Olmert would not be leaving office.
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 at a meeting expected to be held on Thursday, when parliament meets to debate the report on the war.
Separately, Channel 10 reported that Tzipi Livni, the foreign minister, had told her aides that Olmert "must go". Livni is a favourite to succeed Olmert as the leader of Kadima.
Cabel, an entrepreneur and businessman, had little part in the 2006 war and has for several months hinted that he was considering leaving politics, Israeli media 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.
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 Labour 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 duties.