Israel warned today that the aerial attack on Gaza, which has now entered its fourth brutal day, is only “the first of several” military stages intended to wipe out Hamas.

As the army said it was ready to launch a ground incursion and tanks and infantry forces massed on the border, Israeli officials claimed the military “has made preparations for long weeks of action”.

Ehud Olmert, the Israeli Prime Minister, upped the stakes further today when he said he had informed Shimon Peres, the country's ceremonial president, that the current aerial phase of the operation was the “the first of several stages approved by the security cabinet”.

Hamas continued to fire rockets back at the Jewish state as Israeli forces carried out a fourth day of attacks on the Gaza Strip, broadening the offensive to include naval as well as aerial bombardments. But as Britain and other nations called for an end to the violence, there were signs that Hamas was feeling the strain with claims that its leader-in-exile was ready to renew a ceasefire that expired ten days ago.

Rhetoric from Jerusalem has hardened, however, with Meir Sheetrit, the Interior Minister, claiming “there is no room for a ceasefire” with Hamas until the threat of rocket fire had been removed.

Fires burned across Gaza City today where five government buildings were badly damaged in air attacks after Israel pledged to destroy any building with links to Hamas. The Islamists took lone control of Gaza after launching military action to force out the group's rival Fatah, with which it had formed a unity government, in a military coup in summer 2007. Hamas won elections the previous year, but has been shunned by the West for refusing to renounce terrorism or follow the peace process.

Targets hit by Israel in Gaza included a university building, the Interior Ministry and the office of Ismail Haniya, the Hamas political leader. The Palestinian death toll reached 360, with at least 1,550 wounded, in just four days.

Most of the Palestinian victims have been Hamas security forces but at least 64 of them were civilians, according to UN figures. The toll includes two sisters, aged 4 and 11, who died in an airstrike on a rocket squad in northern Gaza this morning.

Four Israelis have been killed by Palestinian rockets since the Israeli attack was launched on Saturday.

“The goal of the operation is to topple Hamas,” Haim Ramon, the deputy to Ehud Olmert, the Prime Minister, said.

It was the first time since it launched its blistering offensive that Israel has openly stated that regime change is its ultimate goal. “We will stop firing immediately if someone takes the responsibility of this government, anyone but Hamas,” Mr Ramon said. “We are favourable to any other government to take the place of Hamas.”

It was not clear which party could take control if Israel succeeds in removing the Islamists. The only other party with experience of rule is Fatah but it is still widely seen by Gazans as corrupt and ineffective. Fatah retains control of the West Bank.

Ehud Barak, the Defence Minister, said Israel was in an “all-out war against Hamas”, while Brigadier-General Dan Harel, the Israeli deputy chief of staff, said that his forces would erase every trace of Hamas from Gaza’s crowded cities.

“After this operation there will not be a single Hamas building left standing in Gaza, and we plan to change the rules of the game,” the general said.

“We are hitting not only terrorists and launchers, but also the whole Hamas Government and all its wings. We are hitting government buildings, production factories, security wings and more.”

That broadening of the offensive was evident in the targets hit yesterday: the Islamic University in Gaza, a hotbed of support for Hamas but also a major educational establishment for students forbidden by Israel from studying outside Gaza, was crushed by bombs. Israel said that its laboratories had been used to improve the crude rockets that Hamas and other militant groups fire into Israel’s southern towns.

Israeli bombers also hit the Interior Ministry, the first time in the campaign that it has struck general government buildings, and a further sign that it is determined to prise Hamas’s fingers from all levers of control in Gaza. Along Gaza’s borders, the Israeli military continued to muster tanks and troops in preparation for a ground offensive that many fear would plunge the strip – home to 1.5 million Palestinian refugees – into even more bloody chaos.

There were signs of cracks in the Arab unity that has been calling on Israel to halt its offensive, but which is wary of Hamas’s Islamist radicalism.

Egypt, which brokered a now defunct ceasefire between Israel and Hamas, said that an Arab summit planned for Friday in Qatar was now in doubt. “Staging an Arab summit could be dangerous and subject to criticism, especially if it does not result in practical measures,” Ahmed Abul Gheit, the Egyptian Foreign Minister, said.

He also launched an attack on Iran, the Shia state known to support and arm Hamas and Hezbollah, in southern Lebanon. In a message aimed at Hezbollah leader Sayyed Hassan Nasrallah on Egyptian television, he said: “You are a man who used to enjoy respect, but you have insulted the Egyptian people.”

The Egyptian newspaper al-Ahram also hinted that Hamas was at least partly to blame for invoking the wrath of Israel with its constant rocket attacks, which appear to serve no strategic purpose. “If you can’t kill the wolf, don’t pull its tail,” it commented.

There were also indications that, behind the public calls for suicide bombings and renewed uprisings, Hamas’s own will was strained.

In Senegal, which currently presides over the Organisation of the Islamic Conference, the Foreign Ministry said that the Hamas leader-in-exile, Khaled Mashal, had declared that he was ready to renew the ceasefire if Israel ended its bombardment and allowed supplies into Gaza.

Hamas was quick to deny the report. It has continued to fire rockets into Israel, one of which killed an Arab Israeli construction worker in the southern city of Ashkelon. A missile hit a bus station in the town of Ashdod, killing a woman and seriously wounding two people. Another Hamas missile killed one person in the kibbutz of Nahal Oz. Israel said that Hamas’s longer-range rockets now threaten half a million of its citizens.

More than 60 Israeli missiles were fired yesterday, but an Israeli army spokesman said that was less than had been expected at this stage in an operation that could last several more days or even weeks. Israeli officials warned that a bloody ground invasion was still on the cards. “The worst . . . is still ahead of us,” General Harel said.

David Miliband, the Foreign Secretary, hardened Britain’s response by warning that the blitz on Gaza could encourage further extremism: “There is no point in me denying my fear that this will fuel radicalism. That is one of the dangers we face at the moment.” Mr Miliband is one of several European Union foreign ministers meeting in Paris tonight for urgent talks on the crisis.

Fears of radicalism appeared to be borne out by Palestinians. “Now there is more hate and radicalism in the Gaza streets,” one young Gazan told The Times by telephone from the apartment where he and his family were huddled, only venturing out to queue for hours for bread in the city’s almost bare shops.

In Iran, a hardline student group started recruiting volunteers to fight Israel after the country’s supreme religious leader, Ayatollah Ali Khamenei, said that anyone who died in the defence of Gaza would be deemed a martyr.