The deaths of 11 Palestinian civilians – nine from one family – in an air strike on Sunday – drew more international calls for an end to six days of hostilities and could test Western support for an offensive Israel billed as self-defence after years of cross-border rocket attacks.

Israel’s military did not immediately comment on a report in the liberal Haaretz newspaper that it had mistakenly fired on the Dalu family home, where the dead spanned four generations, while trying to kill a Hamas rocketry chief.

United Nations Secretary-General Ban Ki-moon was due to arrive in Cairo to weigh in on ceasefire efforts led by Egypt, which borders both Israel and Gaza and whose Muslim Brotherhood-rooted government has been hosting leaders of Hamas and Islamic Jihad, a smaller armed faction in the Palestinian enclave.

Israeli media said a delegation from Israel had also been to Cairo for the truce talks. A spokesman for Prime Minister Benjamin Netanyahu’s government declined comment on the matter.

Italian Foreign Minister Giulio Terzi, speaking in Brussels ahead of a meeting of European Union foreign ministers, said: “I believe there are the conditions to quickly reach a ceasefire in the next few hours.”

He said that from his conversations with members of the Israeli government, he understood “there is no interest at all” to invade the Gaza Strip.

“Exactly the opposite is true,” Terzi said. “Obviously, this Israeli self-restraint should rely on a guarantee that the launches of rockets should end.”

China on Monday urged both sides to halt the violence, while

US President Barack Obama said at the weekend it would be “preferable” if Israel did not mount a ground invasion of Gaza.

The Gaza flare-up, and Israel’s repeated signalling that it could soon escalate from the aerial campaign to a ground sweep of the cramped and impoverished territory, have stoked the worries of world powers watching an already combustible region.

In the absence of any prospect of permanent peace between Israel and Hamas and other Islamist factions, mediated deals for each to hold fire unilaterally have been the only formula for stemming bloodshed in the past. But both sides now placed the onus on the other.

Izzat Risheq, aide to Hamas politburo chief Khaled Meshaal, wrote on Facebook that Hamas would enter a truce only after Israel “stops its aggression, ends its policy of targeted assassinations and lifts the blockade of Gaza”.

Listing Israel’s terms, Vice Prime Minister Moshe Yaalon 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.”

Yaalon also said Israel wanted an end to Gaza guerrilla activity in the neighbouring Egyptian Sinai, a desert peninsula where lawlessness has spread during Cairo’s political crises.

Israel bombed some 80 sites in Gaza overnight, the military said, adding in a statement that targets included “underground rocket launching sites, terror tunnels and training bases” as well as “buildings owned by senior terrorist operatives”.

Netanyahu has said he had assured world leaders that Israel was doing its utmost to avoid causing civilian casualties in Gaza. At least 22 of the Gaza fatalities have been children, medical officials said.

China, which has cultivated good ties with Israel, said on Monday it was extremely concerned about the Israeli military operations in Gaza.

“We condemn the over-use of force causing deaths and injuries amongst innocent ordinary people,” Foreign Ministry spokeswoman Hua Chunying told a daily news briefing in Beijing.

Before leaving for Cairo, Ban urged Israel and the Palestinians to cooperate with all Egyptian-led efforts to reach an immediate ceasefire.

In scenes recalling Israel’s 2008-2009 winter invasion of Gaza, tanks, artillery and infantry have massed in field encampments along the sandy, fenced-off border and military convoys moved on roads in the area.

Israel has also authorised the call-up of 75,000 military reservists, so far mobilising around half that number.

A big, bloody rocket strike might be enough for Netanyahu to give a green light for a ground offensive, despite the political risks of heavy casualties before a January election he is favoured to win.

But while 84 per cent of Israelis supported the Gaza assault, according to a Haaretz poll, only 30 per cent wanted an invasion. Nineteen per cent wanted their government to work on securing a truce soon.

Israel’s declared goal is to deplete Gaza arsenals and force Hamas to stop rocket fire that has bedevilled Israeli border towns for years.

The rockets now have greater range, becoming a strategic weapon for Gaza’s otherwise massively outgunned militants. Several projectiles have targeted Tel Aviv and Jerusalem. None hit the two cities and some of the rockets were shot down by Israel’s Iron Dome interceptor system.

As a precaution against the rocket interceptions endangering nearby Ben-Gurion International Airport, civil aviation authorities said on Monday new flight paths were being used.

There was no indication takeoffs and landings at Ben-Gurion had been affected.

Hamas and other groups in Gaza are sworn enemies of the Jewish state which they refuse to recognise and seek to eradicate, claiming all Israeli territory as rightfully theirs.

Hamas won legislative elections in the Palestinian Territories in 2006 but a year later, after the collapse of a unity government under President Mahmoud Abbas the Islamist group seized control of Gaza in a brief and bloody civil war with forces loyal to Abbas.

Abbas then dismissed the Hamas government led by the group’s leader Ismail Haniyeh but he refuses to recognise Abbas’ authority and runs Gazan affairs.

While it is denounced as a terrorist organisation in the West, Hamas enjoys widespread support in the Arab world, where Islamist parties are on the rise.

US-backed Abbas and Fatah hold sway in the Israeli-occupied West Bank from their seat of government in the town of Ramallah. The Palestinians seek to establish an independent state in the West Bank and the Gaza Strip with East Jerusalem as its capital.