Thick black smoke rose over the city of Gaza as fighting raged on in the Hamas-ruled territory in defiance of international calls for a ceasefire. Medical workers said about half the Palestinians killed on Sunday were civilians.
"Israel is getting close to achieving the goals it set for itself," Olmert told his cabinet in Jerusalem, giving no timeframe for an end to a campaign launched with the declared aim of ending Hamas rocket attacks.
"But patience, determination and effort are still needed to realise these goals in a manner that will change the security situation in the south," Olmert said, referring to Israeli towns where life has been seriously disrupted by rocket salvoes.
On the usually quiet Israeli-occupied Golan Heights, shots were fired from Syria at Israeli army engineers working on the frontier fence, but no one was hurt and it was not immediately clear who was responsible, an Israeli military spokesman said.
Backed by helicopter gunships, Israeli troops and tanks pushed into eastern and southern parts of the city of Gaza, confronting Hamas militants who fired anti-armour missiles and mortar bombs.
At the edge of the city, Mahmoud Abu Hasseera surveyed the rubble of his house, in an area where Israeli tanks and infantry had battled Palestinian fighters hours earlier.
"Where should we and our children go to sleep? To the streets?" he asked. "We have no mattresses, blankets, cooking gas, food or water. Everything was destroyed."
The Palestinian death toll since Israel's offensive began on Dec. 27 stands at 874, many of them civilians, Gaza medical officials said. More than 3,000 Palestinians have been wounded.
Thirteen Israelis—three civilians hit by rocket fire and 10 soldiers—have been killed, Israel says.
Hamas leader Khaled Meshaal said his ruling Islamist group would not consider a ceasefire until Israel ended its air, sea and ground assault and lifted its blockade of Gaza. A Hamas delegation held talks in Cairo on an Egyptian truce plan.
Israel, describing as unworkable a U.N. Security Council resolution calling for a ceasefire, wants a halt to rocket attacks and arrangements to ensure that Hamas cannot rearm through tunnels under the Egypt-Gaza border.
An Israeli defence official was to visit Egypt on Monday to press for tougher anti-smuggling measures.
Street Fighting
New street fighting in the Gaza Strip killed 10 gunmen, medical workers said. Israeli air strikes killed three fighters and a member of the Hamas police force.
Medical officials said Israeli forces had killed 15 civilians, including four members of one family, and Israeli shelling of two villages south of the city of Gaza had set 15 houses on fire.
Israel's military said it attacked a mosque used to store weapons, 10 squads of gunmen, three rocket-launching sites and the house of a Hamas commander.
Fewer rockets have been fired into Israel, but two struck Beersheba, 42 km (26 miles) from the Gaza Strip, and at least four hit other communities, police said. There was some damage but no casualties.
Along Gaza's border with Egypt, Israeli aircraft pounded suspected tunnels. Witnesses said Israeli warplanes have been flying over Egyptian territory during their bombing runs. An Israeli military spokesman had no immediate comment.
The spokesman said Israel had lodged a complaint with a U.N. monitoring force about the shooting on the Golan Heights.
Israel captured the plateau in the 1967 Middle East war and later annexed it in a move not recognised internationally.
In Washington, U.S. President-elect Barack Obama said in broadcast remarks he would begin the search for Middle East peace immediately on becoming president and the Gaza conflict underscored his determination to become involved early.
In Jerusalem, Cabinet Secretary Oved Yehezkel said Hamas leaders were hiding in Gaza's foreign missions, hospitals and bunkers to elude Israeli forces. He did not name the missions.
The Israeli cabinet was expected to discuss a possible "third stage" of the offensive in which the military would storm into Gaza's urban areas, a politically risky move a month before Israel's national election.
Israeli actions have been denounced by the Red Cross, U.N. agencies and Arab and European governments.
New York-based Human Rights Watch has called on Israel to stop using white-phosphorus munitions in densely populated areas in the Gaza Strip, saying it could severely burn people and set structures and fields on fire.
The group said the apparent use of white phosphorus to create smoke screens was "a permissible use in principle under international law".
But it noted media photographs of air-bursting white phosphorus projectiles, which it said can spread burning matter over an area of up to 250 metres (820 ft) in diameter. Israel said it uses only weapons permitted by international law.