The vote was nine in favor with three abstentions on sending troops deeper into southern Lebanon with a mission of finding and destroying the Katyusha missile launchers that have been raining shells into northern Israel for 29 days, Ynetnews reported.
Going into the meeting, Olmert expressed concern the country would be seen as undermining diplomatic efforts under way at the United Nations, as well as driving Israeli casualty counts far higher, Ha'aretz reported.
National Infrastructure Minister Eli Yishai said the timing of the offensive had not yet been set, but expected it would last at least a month.
"We are in a war and there is a need to expand operations. It's correct to act in a more wide-scale manner," he said.
More than 700 people in Lebanon have been killed in the fighting, and Israeli deaths number slightly more than 100.