Israeli troops and tanks were engaged in heavy fighting with Hamas militants last night after Israel followed up its eight-day air assault on Gaza with a ground offensive. The attack, backed by military helicopters, had been preceded by a heavy artillery bombardment.

Columns of tanks, some firing their weapons, crossed the boundary fence from three directions into northern Gaza under darkness. TV networks showed troops, marching in single file, crossing into Gaza, and gun battles could be heard.

Several hours into the armoured offensive, Israeli tanks had moved just over a mile into northern Gaza, according to witnesses, taking up positions in an area frequently used by militants to fire rockets across the border. A Palestinian petrol station along the invasion route was engulfed in flames after being hit by a tank shell. A spokesman for the Israeli forces predicted that the operation would take "many long days". Tens of thousands of reservists have been called up.

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The move was almost immediately met with largely unanimous international condemnation, with the United Nations hastily arranging an overnight emergency session and Secretary-General Ban Ki Moon calling for "an immediate end" to the operation.

The United States also warned Israel in a statement that while it blamed Hamas for the tension, it had grown "deeply concerned about the humanitarian situation" in Gaza as the tanks rolled in. State Department spokesman Sean McCormack added: "We have expressed our concerns to the Israeli government that any military action needs to be mindful of the potential consequences to civilians ... It is obvious a ceasefire should take place."

In Europe there was hurried diplomacy. Foreign Secretary David Miliband said: "Unfolding events show the urgent need for the immediate ceasefire that we have called for." Sinn Fein leader Gerry Adams said: "The Israeli ground offensive in Gaza, while widely anticipated, will be greeted with horror around the world."

The Israeli land attack began after heavy artillery was used in an urban area – for the first time in two years – to clear the way for its forces; the practice had been stopped after 18 members of a single family died in a barrage in November 2006. Yesterday 10 people were killed when shells hit a mosque packed with 200 people in the northern town of Beit Lahiya during evening prayers. The Israeli military confirmed last night that "large numbers of forces" had entered Gaza at "several points", and a correspondent of the Arabic satellite channel Al-Jazeera reported that ground troops backed by artillery had mounted a series of incursions, from the disused airport close to Rafa in the south to the town of Beit Lahiya in the north.

Major Avital Leibovich, an Israeli military spokeswoman, said the aim was to seize areas from where Hamas was launching rocket attacks on southern Israel. Israeli media quoted unconfirmed witness reports suggesting there were incursions under way elsewhere in Gaza. A Hamas spokesman in Damascus, Mohammad Nazzal, said several Israeli soldiers had been killed in fighting in eastern Gaza, but gave no further details. Israeli forces said they were unaware of any casualties among their soldiers.

Khalil Abu Shamala, the director of a human rights organisation, spoke to The Independent on Sunday from his home in Gaza City. "The city is totally paralysed," he said. "Nobody is leaving their houses or can move from one place to another. There is no electricity, so everyone who has a radio is listening and waiting ... for an announcement from the Israelis. From what I understand we are being bombed by F-16s, and tanks are entering from the north and east of the city. I hear they plan to divide Gaza into three sections to weaken communications. They may also enter from the Egypt border and from the Mediterranean."

More than 10,000 Israeli troops and columns of armour had been massing on the Gaza border for days waiting for the order to go ahead. Israel's Defence Minister, Ehud Barak, said: "The campaign won't be easy and it won't be short," emphasising that the operation entails risking Israeli lives. "I know well the dangers that come with an offensive, and what the heavy price will be. I don't want to fool anyone. The residents of southern Israel will also undergo some tough times." Mr Barak also acknowledged publicly for the first time that Israel was braced against a second front being opened by Hizbollah guerrillas in southern Lebanon launching supportive rocket attacks. "We hope that the northern front will remain calm, but we are prepared for any possibility," he said.

Mr Barak is facing political as well as military risks by authorising the long-debated ground offensive in Gaza. A poll last week showed that while 53 per cent of Israelis favoured continuation of the air attacks, only 19 per cent supported the use of ground troops.

The incursions, and last night's destruction of a mosque, are also likely further to inflame opinion across the Muslim world, which has seen violent demonstrations, leaving 400 dead and more than 2,500 injured. Witnesses said the Ibrahim al-Maqadna mosque was hit by up to three Israeli shells. One of the wounded worshippers, Salah Mustafa, told Al-Jazeera from a hospital that the mosque was packed. Another survivor, Mohammed Raheem, described "a huge noise and then people screaming, covered in blood". The Israeli military said last night they were still checking what led to the deaths.

In yesterday's air strikes, Israeli warplanes destroyed large parts of an American school in north-west Gaza in which one person was reported to have been killed and around a dozen injured. Four others, including Abu Zakaria al-Zamal, a senior commander of Hamas's military wing, died from wounds. He was the second Hamas leader killed in three days. Earlier Israeli diplomatic sources said they "were not holding their breath" that a visit by the French President, Nicolas Sarkozy tomorrow, would lead to a solution. They said that draft peace proposals being put together by the European Union do not make adequate provisions for monitoring Hamas attacks.

Khaled Meshaal, the exiled Hamas leader in Damascus, had given a warning that any ground assault would lead Israel to "a black destiny of dead and wounded". But he added that Hamas was "ready to co-operate with any effort leading to an end to the Israeli offensive against Gaza, lifting the siege and opening all crossings". Mr Meshaal did not mention earlier Hamas demands for the ceasefire to be extended to the West Bank.

The US has signalled that it will be playing a more active role in the drive to achieve a ceasefire. One theory is that although the Americans had given tacit approval to the air strikes, they had warned Israel against a land offensive. The President of the Palestinian Authority, Mahmoud Abbas, and several Arab foreign ministers are flying to New York over the weekend to urge the UN Security Council to adopt a draft resolution that would condemn Israel and demand a halt to its bombing campaign. The US has dismissed it as "unacceptable" and "unbalanced" because it makes no mention of halting the Hamas rocket attacks.