President Obama said he was in touch with players across the region in hopes of halting the fighting, and warned of the risks of Israel expanding its air assault into a ground war. "We're going to have to see what kind of progress we can make in the next 24, 36, 48 hours," Obama said in Thailand.
On the ground, there were no signs of any letup in the fighting as Israel announced it was widening the offensive to target military commanders of the ruling Hamas group.
The Israeli military carried out dozens of air strikes throughout the day, and naval forces bombarded targets along Gaza's Mediterranean coast. Many of the attacks focused on homes where militant leaders or weapons were believed to be.
Palestinian militants continued to barrage Israel with rockets, firing more than 100 on Sunday, and setting off air raid sirens across the southern part of the country. About 40 rockets were intercepted by Israel's U.S.-financed "Iron Dome" rocket-defense system, including two that targeted Tel Aviv. At least 10 Israelis were wounded by shrapnel.
Israel's decision to step up its attacks in Gaza marked a new and risky phase of the operation, given the likelihood of civilian casualties in the densely populated territory of 1.6 million Palestinians. Israel launched the offensive Wednesday in what it said was an effort to end months of intensifying rocket fire from the Hamas-ruled Gaza Strip.
In the day's deadliest violence, the Israeli navy fired at a home where it said a top wanted militant was hiding. The missile struck the home of the Daloo family in Gaza City, reducing the structure to rubble.
Frantic rescuers, bolstered by bulldozers, pulled the limp bodies of children from the ruins as survivors and bystanders screamed in grief. Later, the bodies of the children were laid out in the morgue of Gaza City's Shifa Hospital.
Among the 11 dead were four small children and five women, including an 81-year-old, Gaza health official Ashraf al-Kidra said.
More than a dozen homes of Hamas commanders or families linked to Hamas were struck on Sunday. Though most were empty - their inhabitants having fled to shelter - at least three had families in them. Kidra said 20 of 27 people killed Sunday were civilians, mostly women and children.
Sami Abu Zuhri, a Hamas spokesman, said "the Israeli people will pay the price" for the killing of civilians.
Israel sought to place the blame on militants, saying they were intentionally operating in places inhabited by civilians. The military has released videos and images of what it says are militants firing rockets from mosques, schools, and public buildings.
"Hamas is using the Gaza population as human shields," said Brig. Gen. Yoav Mordechai, the chief Israeli spokesman. "They are exploiting crowded residential urban areas."
He acknowledged, however, that it was not clear whether the militant targeted in Sunday's attack was killed, despite earlier claims of success. "I still don't know what became of him," Mordechai told Channel 10 TV.
The prospect of mounting civilian casualties could change the momentum of Israel's operation. Israel launched the offensive on Wednesday with a lightning airstrike that killed Hamas' military chief. Since then, it has carried out a blistering campaign of more than 1,200 air strikes, targeting suspected rocket storage and launching sites.
Israel also struck two high-rise buildings housing media outlets, damaging the top-floor offices of the Hamas TV station, Al Aqsa, and a Lebanese-based broadcaster, Al Quds TV, seen as sympathetic to the Islamists. Six Palestinian journalists were wounded, including one who lost a leg, the Gaza press association said.
Foreign broadcasters, including British, German and Italian TV outlets, also had offices in the buildings.
Lt. Col. Avital Leibovich, an Israeli military spokeswoman, said the strikes targeted Hamas communications equipment on the rooftops. She accused the group of using journalists for cover.
Israeli officials expressed readiness to take the offensive even further with a ground invasion of Gaza. Israel has mobilized thousands of forces and columns of armored vehicles along the border ahead of a possible incursion. "The Israeli military is prepared to significantly expand the operation," Israeli Prime Minister Benjamin Netanyahu declared at the start of the weekly cabinet meeting.
The threats come at an important crossroads - with a fateful choice between further escalation or agreeing to a cease-fire with Hamas. Israel and the West consider Hamas, which seized control of Gaza in 2007, to be a terrorist group.
Obama and British Foreign Secretary William Hague cautioned against a potential Israeli ground invasion of Gaza.
Obama blamed Palestinian militants for starting the round of fighting by raining rockets onto Israel and said the United States supported Israel's right to protect itself. "Israel has every right to expect that it does not have missiles fired into its territory," Obama said.