Mr Olmert invoked the spirit of his coma-stricken mentor, Prime Minister Ariel Sharon, and urged the electorate of five million to cast their ballots amid fears that apathy could damage his support base.
His main rivals, leader of the centre-left Labour Amir Peretz, conceded he no longer expected to win the premiership, while chairman of the right-wing Likud, Benjamin Netanyhu, is also facing the prospect of electoral disaster.
Mr Olmert is hoping Tuesday’s ballot will launch phase two of a project, begun by Mr Sharon with his pullout from Gaza, that would see Israel evacuate isolated West Bank enclaves and cement its hold over the big settlement blocs.
Addressing the cabinet from next to the vacant seat Mr Sharon occupied in the weekly meetings until his January brain haemorrhage, Mr Olmert said the comatose leader would continue to influence the path of the country for years to come.
"Even as we are on the threshold of new elections and the subsequent formation of a new government, there is no doubt that the spirit and path of Arik Sharon will continue to an important component in the public and diplomatic affairs of the State of Israel for years to come," he said.
Two opinion polls published just before an official ban on media campaigning came into effect put Mr Olmert's Kadima party on track to win 34 or 36 seats in the 120 member parliament, albeit fewer than in some earlier polls.
Mr Peretz is predicted to win 18 or 19 seats, but the final poll broadcast on Channel Two television predicted disaster for Mr Netanyahu and surging fortunes for the extreme right-wing Yisrael Beitenu party.