* More Gaza rockets at Tel Aviv are intercepted
* Egypt moves to broker ceasefire; Israel threatens invasion
* Israel says if rockets, attacks stop, it won't attack
GAZA/JERUSALEM, Nov 18 (Reuters) - An Israeli missile killed at least 11 Palestinian civilians including four children in Gaza on Sunday, medical officials said, apparently an 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.
Egypt has taken the lead in trying to broker a ceasefire and Israeli media said a delegation from Israel had been to Cairo for talks on ending the fighting, although a government spokesman declined to comment on the matter.
Egyptian President Mohamed Mursi met Hamas political leader Khaled Meshaal and Islamic Jihad's head Ramadan Shallah as part of the mediation efforts, but a presidency statement did not say if they were conclusive.
Izzat Risheq, a close aide to Meshaal, wrote in a Facebook message that Hamas would agree to a ceasefire only after Israel "stops its aggression, ends its policy of targeted assassinations and lifts the blockade of Gaza".
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."
Gaza health officials said 72 Palestinians , 21 of them children and several women have been killed in Gaza since Israel's offensive began. Hundreds have been wounded.
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.
U.S. 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.
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.
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 Abayah was killed, "but the outcome was that there were civilian casualties". He made no direct mention of the destroyed dwelling.
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 on Sunday, 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, once in the morning and another after dark.
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.
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.
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.
OBAMA CAUTIONS AGAINST GROUND CAMPAIGN
At a news conference during a visit to the Thai capital Bangkok, 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.
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.
Diplomatic efforts continued on Sunday when French Foreign Minister Laurent Fabius met Israeli officials and Palestinian President Mahmoud Abbas in the West Bank.
"It is absolutely necessary that we move urgently towards a ceasefire, and that's where France can be useful," Fabius told French television, adding that war must be avoided.
U.N. Secretary-General Ban Ki-moon will be in Egypt on Monday for talks with Mursi, the foreign ministry in Cairo said. U.N. diplomats earlier said Ban was expected in Israel and Egypt this week to push for an end to the fighting.
Israel's operation has so far drawn Western support for what U.S. 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.