|Livni, left, has called for Olmert to resign[AFP]|
During a special parliamentary session to discuss the scathing Winograd commission's report, Netanyahu said: "We have to go back to the people and let them have their say."
"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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However Olmert's governing coalition has held together, with little apparent appetite among its members for an election.
On Wednesday, Olmert dismissed a public call to resign from Tzipi Livni, the foreign minister, and won critical support from loyalists in their Kadima party.
But Jacky Rowland, Al Jazeera's correspondent in Tel Aviv, said the real test for Olmert will come with Thursday’s demonstrations.
Rowland said the rally would be apolitical and that many Israelis are simply sick and tired of politicians and politics.
Exactly how many people turn out could determine whether Olmert remains in power or decides to resign.
"Our message will be that leaders who make mistakes that cost lives should put their keys on the table and go," said Mickey Leibovitch, an organiser of the rally.
Olmert accepted responsibility for "many mistakes" during the war against Hezbollah last summer.
But he said he would not resign, insisting he was the best man to put things right - an argument Netanyahu challenged."Those who failed at war cannot be the ones who correct the failures," he told parliament.
Source: Al Jazeera and agencies