At an emergency cabinet meeting earlier on Wednesday, Olmert acknowledged personal failings.
|"I suggest that all those who are in a hurry to take advantage of this report and make political gain - slow down"|
Ehud Olmert, Israeli prime minister
He said: "It is primarily incumbent on this government, which is responsible for the failings, to also be responsible for fixing them.
"I suggest that all those who are in a hurry to take advantage of this report and make political gain - slow down."
Dan Halutz, former Israeli military chief, stepped down earlier this year, and aides to Amir Peretz, Israel's defence minister, told Israel Radio and Army Radio he was considering stepping down.
Future political landscape
Opinion polls in three major Israeli newspapers showed 65 to 73 per cent of the public wanted Olmert to quit.
The two frontrunners to replace Olmert are Livni, 48, and
Benjamin Netanyahu, former prime minister, of the Likud party.
Despite growing dissent within Kadima, Olmert's main coalition partners, notably the Labour group, have so far stuck by him, apparently keen to avoid an early election that could end up reducing their parliamentary power.