Israeli soldiers peer out of their tank as they move toward the Gaza Strip from southern Israel early today. Israeli forces pounded Gaza Strip houses, mosques and tunnels, killing at least 13, including children.

GAZA CITY, Gaza Strip — Israel consolidated its hold on parts of the Gaza Strip today, seizing high-rise buildings on the outskirts of the territory's biggest city as a stream of world leaders headed for the region to press for a truce. At least seven Palestinian children were killed, adding to the growing toll of civilian deaths that has caused international outrage.

As the bruising campaign against Gaza's Hamas rulers entered its 10th day, the Islamic militant group continued to pummel southern Israel with rockets.

Israeli Defense Minister Ehud Barak said the offensive would continue until Israel achieved "peace and tranquility" for residents of southern Israel. Militants, defying the attacks, fired more than two dozen rockets by midday, and Hamas' strongman urged Palestinians to "crush" the invading Israeli forces and target Israeli civilians.

After a weeklong air offensive, Israeli ground troops invaded Gaza late Saturday. The Israelis have seized a main highway in Gaza, slicing the territory in half. Israeli forces also pounded houses, mosques and smuggling tunnels today as they pressed forward with the offensive.

The Israeli army said "dozens" of militants have been killed or wounded.

Gaza health officials reported 537 Palestinian dead and nearly 2,000 wounded since Israel embarked upon the campaign Dec. 27. At least 200 civilians were among the dead.

Israel has three main demands: an end to Palestinian attacks, international supervision of any truce and a halt to Hamas rearming.

Hamas demands a cessation of Israeli attacks and the opening of vital Gaza-Israel cargo crossings, Gaza's main lifeline.

Israeli forces seized sparsely populated areas in northern Gaza and by this morning were dug in on the edges of Gaza City. Further movement into the heart of the built-up areas would mean deadly urban warfare, with house-to-house fighting, sniper fire and booby traps in crowded streets and alleyways familiar to Hamas' 20,000 fighters.

Thirteen civilians died in the various attacks across Gaza this morning, said Gaza health official Dr. 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, he said. Three other adult civilians died in attacks elsewhere.

Israeli troops seized three six-story buildings on the outskirts of Gaza City, taking up rooftop positions after locking residents in rooms and taking away their cell phones, a neighbor said, quoting a relative in one of the buildings before his phone was taken away.

"The army is there, firing in all directions," said Mohammed Salmai, a 29-year-old truck driver. "All we can do is take clothes to each other to keep ourselves warm and pray to God that if we die, someone will find our bodies under the rubble."

Civilian casualties have spiked since Israel launched a ground offensive Saturday after a week of punishing air strikes. Of about 80 Palestinians killed during the ground operation, at least 70 were civilians, Hassanain said.

If civilians are killed, then Hamas is to blame because it operates within civilian areas, said an Israeli military spokeswoman, Maj. Avital Leibovich.

"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."

Black smoke from tank shells and wind-swept dust billowed in the air over Gaza City, while white smoke from mortar shells rose in plumes above a main road leading to northern Gaza that the Israeli military seized on Sunday, cutting off Gaza's north from its south. Explosions could be heard in Gaza City as aircraft attacked buildings.

The streets of Gaza City, home to 400,000 people, were almost empty. Two children crossing a street near a Hamas security compound didn't bother to look right and left for cars but gazed up at the sky, apparently looking for attack aircraft.