At least seven Palestinian children were killed, and Hamas continued to launch rockets into southern Israel.
As the campaign against Gaza's rulers entered its 10th day, Israel's defense minister said the offensive against Hamas militants in the Palestinian enclave would go on until Israel's security was ensured.
"Hamas has so far sustained a very heavy blow from us, but we have yet to achieve our objective and therefore the operation continues," Israeli Defense Minister Ehud Barak said. Gaza fighters continued to pummel southern Israel with rockets Monday, according to media reports.
After a weeklong air offensive, Israeli ground troops invaded Gaza late Saturday. They have seized a main highway in Gaza, slicing the territory in half. Israeli forces also pounded houses, mosques and smuggling tunnels on Monday as they pressed forward with the offensive.
Gaza health officials reported 537 Palestinians killed and nearly 2,000 wounded since Israel embarked upon the campaign on Dec. 27. At least 200 civilians were reported to be among the dead.
Five Israelis have been killed since the offensive began, including a soldier who died in the ground operation.
Israel has three main demands: an end to Palestinian attacks, an international role in supervising any truce and a halt to Hamas rearming.
Israel on Monday rebuffed European proposals for international observers in the Gaza Strip after any cease-fire, pushing instead for equipment and teams to help search out and destroy smuggling tunnels Hamas could use to rearm, Reuters reported.
Israeli Foreign Minister Tzipi Livni said Monday that Israel was "not only defending its right to defend itself" but was also waging a campaign "against extremism and against terror," the New York Times reported.
Hamas demands a cessation of Israeli attacks and the opening of vital Gaza-Israel cargo crossings, Gaza's main lifeline.
Thirteen civilians died in the various attacks across Gaza on Monday morning, said Gaza health official Moaiya Hassanain.
Four young siblings were killed in a missile strike on a house east of Gaza City. Three other children died in a naval shelling of a Gaza City beach camp, and three adult civilians died when a missile struck near a house of mourning in the northern town of Beit Lahiya, Hassanain said.
Israeli military spokeswoman Maj. Avital Leibovich said Hamas is to blame if civilians are killed because it operates within civilian areas.
"If Hamas chose cynically to use those civilians as human shields, then Hamas should be accountable," she said. "Civilians will probably continue to get killed, unfortunately, because Hamas put them in the first lines of fire."
International efforts to secure a cease-fire moved ahead despite the fighting with French President Nicolas Sarkozy and Middle East special envoy Tony Blair visiting the region.
While blaming Hamas for causing Palestinian suffering with rocket fire that led to the Israeli offensive, Sarkozy has condemned Israel's use of ground troops, reflecting general world opinion. Sarkozy and other diplomats making their way to the region are expected to press hard for a cease-fire.
The Bush administration has supported Israel, saying Hamas must halt rocket fire at Israel for a truce to take shape.
A Hamas official said a delegation from the Islamist group would head for talks in Egypt, which has also opened contacts to achieve a cease-fire. But senior Hamas political leader Mahmoud Zahar urged Hamas forces to fight on "in the name of God."