GAZA CITY, Gaza Strip (AP) -- An Israeli missile flattened a two-story house in a residential neighborhood of Gaza City on Sunday, killing at least 11 civilians, mostly women and children, Palestinian medical officials said, as Israel expanded a military offensive to target homes of wanted militants. The attack, which Israel said targeted a militant, was the single deadliest incident of the five-day-old Israeli operation and hiked a toll Sunday that was already the highest number of civilians killed in one day, according to Gaza medics. The bloodshed is likely to raise international pressure for a cease-fire, with Egypt taking the leading role in mediating between Israel and Hamas. President Barack Obama said he had been in touch with the leaders of Israel, Egypt, and Turkey in an effort to halt the fighting. "We're going to have to see what kind of progress we can make in the next 24, 36, 48 hours," he said. Obama cautioned against a potential Israeli ground invasion into Gaza, warning it could only deepen its death toll. At the same time, he blamed Palestinian militants for starting the round of fighting by raining rockets onto Israel, and he defended Israel's right to defend itself. "Israel has every right to expect that it does not have missiles fired into its territory," Obama said in Thailand at the start of a three-nation tour in Asia. An Israeli envoy arrived in Cairo on Sunday and held talks with Egyptian officials on a ceasefire, according to Egyptian security officials and Nabil Shaath, a top aide of Palestinian President Mahmoud Abbas who was in the Egyptian capital. But Israel and Gaza's militant Hamas rulers remain far apart on any terms for a halt in the bloodshed, which has killed 70 Palestinians - including 36 civilians, according to Gaza health officials - and three Israeli civilians. Hamas is linking a truce deal to a complete lifting of the border blockade on Gaza imposed since Islamists seized the territory by force. Hamas also seeks Israeli guarantees to halt targeted killings of its leaders and military commanders. Israeli officials reject such demands. They say they are not interested in a "timeout," and want firm guarantees that militant rocket fire into Israel will finally end. Past ceasefires have been short lived. As the offensive moved forward, Israel found itself at a crossroads - on the cusp of launching a ground offensive into Gaza to strike an even tougher blow against Hamas, or pursuing Egyptian-led truce efforts. "The Israeli military is prepared to significantly expand the operation," Israeli Prime Minister Benjamin Netanyahu declared at the start of the weekly Cabinet meeting. At the same time, Gaza militants continued their barrage of rocket fire at Israel, firing more than 100, including two at Tel Aviv. More than 10 Israelis were injured by shrapnel, two moderately, according to police spokesman Mickey Rosenfeld. Israel's "Iron Dome" rocket-defense system shot down at least 30 rockets, including the ones aimed at Tel Aviv.