At least 11 Palestinian civilians, including four children, were killed yesterday in what Hamas said was an Israeli air strike on a Gaza apartment building.

It is the highest death toll in a single incident in five days of a campaign Israel says is intended to stop Palestinian rocket fire into the Jewish state.

It came as Israel signalled a possible ground invasion of the Hamas-run enclave as the next stage in its offensive, and spelled out its conditions for a truce.

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US President Barack Obama said while Israel had a right to defend itself against rockets, it would be "preferable" to avoid a military thrust into the densely populated Gaza Strip. Such an assault would risk high casualties and international outcry.

A spokesman for the Hamas-run Interior Ministry said an Israeli missile wrecked the three-storey residential building, killing 11 people, all of them civilians. Four women and four children were among the dead.

Israeli Prime Minister Benjamin Netanyahu had earlier assured world leaders Israel was doing its utmost to avoid causing civilian casualties.

For their part, Gaza militants launched dozens of rockets into Israel, targeting its commercial capital, Tel Aviv, for a fourth day.

"The massacre of the Dalu family will not pass without punishment," Hamas's armed wing said in a statement.

The Jewish state's "Iron Dome" missile shield shot down two of the rockets fired toward Tel Aviv, Israel's biggest city, but falling debris from the interception hit a car, which caught fire. Its driver was not hurt.

In scenes recalling Israel's 2008-2009 winter incursion into Gaza, tanks, artillery and infantry massed in field encampments along the border. Military convoys moved on roads after they were closed to civilian traffic.

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.

Gaza health official Mufid al-Miklalati said 65 Palestinians – half of them women and children – had been killed in Gaza since the Israeli offensive began, with hundreds wounded.

More than 500 rockets fired from Gaza have hit Israel since Wednesday, killing three civilians and wounding dozens.

Israel's declared goal is to force Islamist Hamas to stop rocket fire that, with increased range, now threatens Tel Aviv and Jerusalem. Israel withdrew from Gaza in 2005. Two years later Hamas took control of the enclave, which the Israelis have kept under blockade.

At a news conference during a visit to Bangkok, Mr Obama said Israel has "every right to expect that it does not have missiles fired into its territory".

"If this can be accomplished without a ramping up of military activity in Gaza, that is preferable," he said.

"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."

Mr Obama has been in regular contact with Egyptian and Turkish leaders to ask for help in stopping rocket barrages by 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.

Witnesses said two Gaza City media buildings were hit in other air raids on Sunday. Eight journalists were wounded and facilities belonging Britain's Sky News and Hamas's Al-Aqsa TV were damaged.

An employee of the Beirut-based al Quds television station lost his leg in the attack.

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.

Egyptian President Mohamed Mursi's security deputies sought to broker a truce with Hamas leaders. The Egyptian leader said: "There are some indications that there is a possibility of a ceasefire soon, but we do not yet have firm guarantees".

Egypt mediated previous ceasefire deals between Israel and Hamas, the latest of which has unravelled with recent violence.

UN Secretary-General Ban Ki-moon will be in Egypt on Monday for talks with Mr Mursi, and the head of the Arab League and a group of Arab foreign ministers will visit Gaza on Tuesday to show solidarity with the Palestinians.

Listing Israel's terms for ceasing fire, Moshe Yaalon, a 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."

Foreign Minister William Hague said he and Prime Minister David Cameron "stressed to our Israeli counterparts that a ground invasion of Gaza would lose Israel a lot of the international support and sympathy that they have."

Israel's cabinet decided on Friday to double the current reserve-troop quota set for the Gaza campaign to 75,000.

The last Gaza war, a three-week Israeli blitz and invasion four years ago, killed 1400 Palestinians, mostly civilians. Thirteen Israelis died in the conflict.