An Israeli missile has killed at least 11 people in Gaza, medical officials said, in an apparent attack on a top militant that brought a three-storey home crashing down.
International pressure for a ceasefire seemed certain to mount in response to the deadliest single incident in five days of Palestinian rocket attacks on Israel and Israeli air strikes on the Gaza Strip.
Israel's chief military spokesman said Yihia Abayah, a senior commander of rocket operations in the Gaza Strip, had been the target.
The spokesman, Yoav Mordechai, told Israel's Channel 2 television he did not know whether Mr Abayah was killed, "but the outcome was that there were civilian casualties".
He made no direct mention of the destroyed dwelling.
A spokesman for the Hamas-run Interior Ministry said 11 people, all of them civilians, were killed when an Israeli missile flattened the home of the Dalu family. Medics said four women and four children were among the dead.
Earlier Israel gave off signs of a possible ground invasion of the Hamas-run enclave as the next stage in its offensive, billed as a bid to stop Palestinian rocket fire into the Jewish state.
It also spelt out its conditions for a truce.
US President Barack Obama said that while Israel had a right to defend itself against the salvoes, it would be "preferable" to avoid a military thrust into the Gaza Strip, a narrow, densely populated coastal territory.
Such an assault would risk high casualties and an international outcry.
Prime Minister Benjamin Netanyahu said earlier that he had assured world leaders that Israel was doing its utmost to avoid causing civilian casualties in the military showdown with Hamas.
"The massacre of the Dalu family will not pass without punishment," Hamas's armed wing said in a statement.
In other air raids, two Gaza City media buildings were hit, witnesses said.
Eight journalists were wounded and facilities belonging to Hamas's Al-Aqsa TV as well as Britain's Sky News were damaged.
An employee of the Beirut-based al Quds television station lost his leg in the attack, local medics said.
The Israeli military said the strike targeted a rooftop "transmission antenna used by Hamas to carry out terror activity", and that journalists in the building had effectively been used as human shields by Gaza's rulers.
For their part, Gaza militants launched dozens of rockets into Israel and targeted its commercial capital, Tel Aviv, for a fourth day with one attack in the morning and another after nightfall.
Israel's "Iron Dome" missile shield shot down all three rockets, but falling debris from the daytime interception hit a car, which caught fire. Its driver was not hurt.
In scenes recalling Israel's 2008-2009 winter invasion of Gaza, tanks, artillery and infantry massed in field encampments along the sandy, fenced-off border. Military convoys moved on roads in the area newly closed to civilian traffic.
Mr Netanyahu said Israel was ready to widen its offensive.
"We are exacting a heavy price from Hamas and the terrorist organisations and the Israel Defence Forces are prepared for a significant expansion of the operation," he said at a cabinet meeting, giving no further details.
Gaza health officials said 69 Palestinians - about half of them women and children - have been killed in Gaza since the Israeli offensive began, with hundreds wounded.
The Israeli military said 544 rockets fired from Gaza have hit Israel since Wednesday, killing three civilians and wounding dozens. Some 302 were intercepted and 99 failed to reach Israel and landed inside the Gaza Strip, it added.
Israel's declared goal is to deplete Gaza arsenals and force the Islamist Hamas to stop rocket fire that has bedevilled Israeli border towns for years and is now displaying greater range, putting Tel Aviv and Jerusalem in the crosshairs.
Israel withdrew settlers from Gaza in 2005 and two years later Hamas took control of the impoverished enclave, which the Israelis have kept under blockade.
At a news conference during a visit to the Thai capital Bangkok, Mr Obama said Israel has "every right to expect that it does not have missiles fired into its territory".
He added: "If this can be accomplished without a ramping up of military activity in Gaza that is preferable. That's not just preferable for the people of Gaza, it's also preferable for Israelis because if Israeli troops are in Gaza they're much more at risk of incurring fatalities or being wounded," he said.
Mr Obama said he had been in regular contact with Egyptian and Turkish leaders - to secure their mediation in bringing about a halt to rocket barrages by Hamas and other Islamist militants.
"We're going to have to see what kind of progress we can make in the next 24, 36, 48 hours," he added.
Israeli officials declined to confirm or deny reports that an Israeli negotiator had flown to Cairo to discuss a ceasefire.
Egyptian President Mohamed Mursi said in Cairo, as his security deputies sought to broker a truce with Hamas leaders, that "there are some indications that there is a possibility of a ceasefire soon, but we do not yet have firm guarantees".
Silvan Shalom, one of Mr Netanyahu's deputies, said: "There are contacts, but they are currently far from being concluded."
UN Secretary-General Ban Ki-moon will be in Egypt tomorrow for talks with Mr Mursi, the foreign ministry in Cairo said. UN diplomats earlier said Mr Ban was expected in Israel and Egypt this week to push for an end to the fighting.
Listing Israel's terms for ceasing fire, Moshe Yaalon, another deputy to the prime minister, wrote on Twitter: "If there is quiet in the south and no rockets and missiles are fired at Israel's citizens, nor terrorist attacks engineered from the Gaza Strip, we will not attack."
Israel's operation has so far drawn Western support for what US and European leaders have called its right to self-defence, but there was also a growing number of appeals from them to seek an end to the hostilities.