JERUSALEM, Nov 12 (Reuters/Crispian Balmer) - Sporadic missile fire from the Gaza Strip hit southern Israel on Monday for a fourth straight day, with Egypt trying to secure a truce and Israel warning it was poised to toughen its response.

Prime Minister Benjamin Netanyahu convened foreign ambassadors in what appeared to be an attempt to preempt international censure should Israel, whose 2008-2009 Gaza offensive exacted a costly civilian toll, again go in hard.

Netanyahu briefed the envoys in Ashkelon, a port city within range of some Palestinian rockets. None of their governments would accept a situation like this, he said.

Environment Minister Gilad Erdan, an influential member of Netanyahu's Likud party, said the briefing was meant to prepare world opinion for what is about to happen, adding there might be a major Israeli escalation within a few hours.

Hamas bears responsibility. The heads of Hamas should pay the price and not sleep at night. I expect to see not just a return to targeted killings, but also to very wide activity by (the army), he told Israel Radio.

Gaza is governed by the Islamist movement Hamas, which does not recognize Israel. While it took part in missile launches at the weekend, it did not claim responsibility for Monday's attacks, suggesting it was looking to step back.

The Israeli military said Palestinians had fired 11 rockets in the morning, after more than 110 in the preceding 72 hours.

Netanyahu said a million Israelis - around one-eighth of the population - were in danger. Israel has been deploying its Iron Dome rocket interceptor, air raid sirens and blast shelters, but eight people have still been wounded by the salvos.

Six Palestinians, including four civilians, have been killed by Israeli shells fired on Gaza since Saturday, and 40 wounded.

EGYPT IN THE PICTURE

A Palestinian official who declined to be named said Egypt had been trying to broker a ceasefire between Israel and Palestinian militants and that, although no formal truce was in place, Hamas understood the need for calm.

Monday's launches were claimed by smaller groups, including a radical Salafi organization that rejects Hamas's authority.

Hamas was due to convene other Palestinian factions at 6 p.m. (1600 GMT) to discuss the situation.

Israel has shown little appetite for a new Gaza war, which could strain relations with the new Islamist-rooted government in neighboring Egypt. The countries made peace in 1979.

But Netanyahu may be reluctant to seem weak ahead of a Jan. 22 election that opinion polls currently predict he will win.

Israel said the latest flare-up started on Thursday with a fierce border clash. On Saturday, a Palestinian missile strike wounded four Israeli troops patrolling the boundary, triggering army shelling of Gaza in which the four civilians died.

In turn, dozens of mortars and rockets were launched at Israel, which carried out a series of air strikes in Gaza.

Top-selling Israeli daily Yedioth Ahronoth said the United States had given a green light for an Israeli operation in Gaza.

The political adviser to Ismail Haniyeh, Gaza's prime minister, said he believed Egypt's new president, Mohamed Mursi, provided a safety net for the Palestinians.

The president of the biggest neighboring Arab country (has) said: We will not allow a new war on Gaza, and Palestinian blood is our blood, Youssef Rizqa wrote in the pro-Hamas daily Felesteen. (Additional reporting by Ari Rabinovitch and Maayan Lubell in Jerusalem and Nidal Al-Mughrabi in Gaza)