It is a war on two fronts. Months ago, as Israel prepared to unleash its latest wave of desolation against Gaza, it recognised that blasting Hamas and "the infrastructure of terror", which includes police stations, homes and mosques, was a straightforward task.

Israel also understood that a parallel operation would be required to persuade the rest of the world of the justice of its cause, even as the bodies of Palestinian women and children filled the mortuaries, and to ensure that its war was seen not in terms of occupation but of the west's struggle against terror and confrontation with Iran.

After the debacle of its 2006 invasion of Lebanon - not only a military disaster for Israel, but also a political and diplomatic one - the government in Jerusalem spent months laying the groundwork at home and abroad for the assault on Gaza with quiet but energetic lobbying of foreign administrations and diplomats, particularly in Europe and parts of the Arab world.

A new information directorate was established to influence the media, with some success. And when the attack began just over a week ago, a tide of diplomats, lobby groups, bloggers and other supporters of Israel were unleashed to hammer home a handful of carefully crafted core messages intended to ensure that Israel was seen as the victim, even as its bombardment killed more than 430 Palestinians over the past week, at least a third of them civilians or policemen.

The unrelenting attack on Gaza, with an air strike every 20 minutes on average, has not stopped Hamas firing rockets that have killed four Israelis since the assault began, reaching deeper into the Jewish state than ever before and sending tens of thousands of people fleeing. Last night Israel escalated its action further, as its troops poured across Gaza's border, part of what appeared to be a significant ground invasion. And a diplomatic operation is already in full swing to justify the further cost in innocent lives that would almost certainly result.

Dan Gillerman, Israel's ambassador to the UN until a few months ago, was brought in by the Foreign Ministry to help lead the diplomatic and PR campaign. He said that the diplomatic and political groundwork has been under way for months.

"This was something that was planned long ahead," he said. "I was recruited by the foreign minister to coordinate Israel's efforts and I have never seen all parts of a very complex machinery - whether it is the Foreign Ministry, the Defence Ministry, the prime minister's office, the police or the army - work in such co-ordination, being effective in sending out the message."

In briefings in Jerusalem and London, Brussels and New York, the same core messages were repeated: that Israel had no choice but to attack in response to the barrage of Hamas rockets; that the coming attack would be on "the infrastructure of terror" in Gaza and the targets principally Hamas fighters; that civilians would die, but it was because Hamas hides its fighters and weapons factories among ordinary people.

Hand in hand went a strategy to remove the issue of occupation from discussion. Gaza was freed in 2005 when the Jewish settlers and army were pulled out, the Israelis said. It could have flourished as the basis of a Palestinian state, but its inhabitants chose conflict.

Israel portrayed Hamas as part of an axis of Islamist fundamentalist evil with Iran and Hezbollah. Its actions, the Israelis said, are nothing to do with continued occupation of the West Bank, the blockade of Gaza or the Israeli military's continued killing of large numbers of Palestinians since the pullout. "Israel is part of the free world and fights extremism and terrorism. Hamas is not," the foreign minister and Kadima party leader, Tzipi Livni, said on arriving in France as part of the diplomatic offensive last week.

Earlier in the week Livni deployed the "with us or against us" rhetoric of George W Bush's war on terror. "These are the days when every individual in the region and in the world has to choose a side. And the sides have changed. No longer is it Israel on one side and the Arab world on the other," she said. "Israel chose its side the day it was established; the Jewish people chose its side during its thousands of years of existence; and the prayer for peace is the voice sounded in the synagogues."

It was a message pumped home with receptive Arab governments, such as Egypt and Jordan, which view Hamas with hostility. "Large parts of the Muslim and Arab world realise that Hamas represents a greater danger to them even than it does to Israel. Its extremism, its fundamentalism, is a great danger to them as well," said Gillerman. "We've seen the effect of that in numerous responses, in the public statements made by [Egypt's] President Mubarak and even by [Palestinian president] Mahmoud Abbas and other Arabs. This is totally unprecedented."

Indeed, the Egyptian Foreign Minister, Ahmed Aboul Gheit, said his government knew exactly what was coming: "The signs that Israel was determined to strike Hamas in Gaza for the past three months were clear. They practically wrote it in the sky. Unfortunately they [Hamas] served Israel the opportunity on a golden platter."

Also crucial was what was not said. Just a few months ago Livni was talking of wiping out Hamas, but that would be unpalatable to much of the outside world as a justification for the assault. So now the talk is of pressing Gaza's government to agree to a new ceasefire. Occasionally someone has got off-message. A couple of days into the assault on Gaza, Israel's ambassador to the UN, Gabriela Shalev, said it would continue for "as long as it takes to dismantle Hamas completely". Infuriated Israeli officials in Jerusalem warned her that such statements could set back the diplomatic offensive.

In the first hours of the attack, Israel repeated the same messages to the wider world. Livni and the Labour defence minister, Ehud Barak, were widely quoted on international TV. The government's national information directorate sought to focus foreign media attention on the 8,500 rockets fired from Gaza into Israel over the past eight years and the 20 civilians they have killed, rather than the punishing blockade of Gaza and the 1,700 Palestinians killed in Israeli military attacks since Jewish settlers were pulled out of Gaza three years ago.

Lobby groups, such as the British Israel Communications and Research Centre (Bicom) in London and the Israel Project in America, were mobilised. They arranged briefings, conference calls and interviews. The Israeli military posted video footage on YouTube. Israeli diplomats in New York arranged a two-hour "citizens' press conference" on Twitter for thousands of people. At the same time, Israel in effect barred foreign journalists from witnessing the results of its strategy.

Livni has suggested that Israel's assault is good for the Palestinians by helping to free them from the grip of Hamas. "She's basically trying to convince me that they're doing this for my own good," said Diana Buttu, the Palestinian Liberation Organisation's legal counsel and negotiator with the Israelis over the 2005 pullout from Gaza. "I've had some Israeli friends reiterate the same thing: 'You should be happy that we're rooting out Hamas. They're a problem for you, too.' I don't need her to tell me what's good for me and what's bad for me, and I don't think carrying out a massacre is good for anybody."

And when the killing started, Israel claimed that the overwhelming majority of the 400-plus killed were Hamas fighters and the buildings destroyed part of the infrastructure of terror. But about a third of the dead were policemen. Although the police force in Gaza is run by Hamas, Buttu said Israel is misrepresenting it as a terrorist organisation.

"The police force is largely used for internal law and order, traffic, the drug trade. They weren't fighters. They hit them at a graduation ceremony. Israel wants to kill anyone associated with Hamas, but where does it stop? Are you a legitimate target if you work in the civil service? Are you a legitimate target if you voted for Hamas?" she said.

Similarly, while Israel accuses Hamas of risking civilian lives by hiding the infrastructure of terror in ordinary neighbourhoods, many of the Israeli missile targets are police stations and other public buildings that are unlikely to be built anywhere else.

Israel argues that Hamas abandoned the June ceasefire that Jerusalem was prepared to continue. "Israel is the first one who wants the violence to end. We were not looking for this. There was no other option. The truce was violated by Hamas," said Livni.

However, others say that the truce was thrown into jeopardy in November when the Israeli military killed six Hamas gunmen in a raid on Gaza. The Palestinians noted that it was election day in the US, so most of the rest of the world did not notice what happened. Hamas responded by firing a wave of rockets into Israel. Six more Palestinians died in two other Israeli attacks in the following week.

"They were assaulting Gaza militarily, by sea and by air, all through the ceasefire," said Buttu. Neither did the killing of Palestinians stop. In the nearly three years since Hamas came to power, and before the latest assault on Gaza, Israel forces had killed about 1,300 people in Gaza and the West Bank. While a significant number of them were Hamas activists - and while hundreds of Palestinians have been killed by other Palestinians in fighting between Hamas and Fatah - there has been a disturbing number of civilian deaths.

The Palestinian Centre for Human Rights says that one in four of the victims is aged under 18. Between June 2007 and June 2008, Israeli attacks killed 68 Palestinian children and young people in Gaza. Another dozen were killed in the West Bank.

In February, an Israeli missile killed four boys, aged eight to 14, playing football in the street in Jabalia. In April, Meyasar Abu-Me'tiq and her four children, aged one to five years old, were killed when an Israeli missile hit their house as they were having breakfast. Even during the ceasefire, Israel killed 22 people in Gaza, including two children and a woman.

Perhaps crucial to the ceasefire's collapse were the differing views of what it was supposed to achieve. Israel regarded the truce as calm in return for calm. Hamas expected Israel to lift the blockade of Gaza that the latter said was a security response to the firing of Qassam rockets.

But Israel did not end the siege that was wrecking the economy and causing desperate shortages of food, fuel and medicine. Gazans concluded that the blockade was not so much about rocket attacks as punishment for voting for Hamas.

Central to the Israeli message has been that, when it pulled out its military and Jewish settlers three years ago, Gaza was offered the opportunity to prosper. "In order to create a vision of hope, we took out our forces and settlements, but instead of Gaza being the beginning of a Palestinian state, Hamas established an extreme Islamic rule," said Livni. Israeli officials argue that Hamas, and by extension the people who elected it, was more interested in hating and killing Jews than building a country.

Palestinians see it differently. Buttu says that from the day the Israelis withdrew from Gaza, they set about ensuring that it would fail economically. "When the Israelis pulled out, we expected that the Palestinians in Gaza would at least be able to lead some sort of free life. We expected that the crossing points would be open. We didn't expect that we would have to beg to allow food in," she said.

Buttu notes that even before Hamas was elected three years ago, the Israelis were already blockading Gaza. The Palestinians had to appeal to US secretary of state Condoleezza Rice and James Wolfensohn, the president of the World Bank, to pressure Israel to allow even a few score of trucks into Gaza each day. Israel agreed, then reneged. "This was before Hamas won the election. The whole Israeli claim is one big myth. If there wasn't already a closure policy, why did we need Rice and Wolfensohn to try to broker an agreement?" asked Buttu.

Yossi Alpher, a former official in the Mossad intelligence service and an ex-adviser on peace negotiations to the then prime minister, Ehud Barak, said the blockade of Gaza is a failed strategy that might have strengthened Hamas. "I don't think anyone can produce clear evidence that the blockade has been counterproductive, but it certainly hasn't been productive. It's very possible it's been counterproductive. It's collective punishment, humanitarian suffering. It has not caused Palestinians in Gaza to behave the way we want them to, so why do it?" he said. "I think people really believed that, if you starved Gazans, they will get Hamas to stop the attacks. It's repeating a failed policy, mindlessly."