Israel has sent ground forces into the Gaza Strip after a week of air strikes to try to halt rocket attacks by Palestinian militants.
Its troops were reported to be engaged in heavy clashes with Hamas fighters in northern Gaza. Both sides have reported casualties in the fighting.
The UN secretary general called for an immediate halt to operations.
But an emergency Security Council meeting failed to agree a united approach to the Gaza conflict.
As dawn broke in Gaza a large plume of black smoke could be seen rising from part of the northern strip while the sound of exploding artillery shells - could also be heard. The shelling had continued through the night.
Hamas has held the people of Gaza hostage ever since their illegal coup against the forces of (Palestinian) President Mahmoud Abbas
Witnesses say Israeli military convoys supported by attack helicopters crossed into northern Gaza at four separate points after nightfall on Saturday.
Advancing Israeli tanks were reported to be in battles around Gaza City and the northern towns of Beit Lahiya and Jabaliya, the Afp news agency reported. Hamas fighters replied with mortars and rockets, witnesses said.
The Israeli army said 30 of its soldiers had been wounded in the ground offensive, two of them seriously.
Palestinian medical officials said eight Gazans had been killed by Israeli troops, five of them gunmen.
An Israeli military spokeswoman said the objective of the ground operation was "to destroy the Hamas terror infrastructure in the area of operations".
"We are going to take some of the launch areas used by Hamas," Maj Avital Leibovitch told reporters.
Israeli officials have described the offensive as a "limited" operation.
The move into Gaza had been preceded by some of the heaviest Israeli air and artillery attacks on the territory in more than a week of bombardment.
Defence Minister Ehud Barak said the ground campaign against Hamas "will not be easy or short, but we are determined".
"Our aim is to force Hamas to stop its hostile activities against Israel and Israelis from Gaza, and to bring about a significant change in the situation in the southern part of Israel," he told a news conference.
"We have carefully weighed all our operations. We are not war-hungry, but we shall not allow a situation in which our towns, villages and civilians are constantly targeted by Hamas."
Mr Barak also said Israel would "keep a sensitive eye" on its northern border with Lebanon, where it fought a short but bloody war with the Shia Hezbollah movement in 2006.
"We hope the situation will remain calm. Nevertheless, we are ready and alert to face any unwanted development in that area," he added.
The BBC's Paul Wood in Jerusalem says this is probably just the first wave of the assault, since there are said to be some 10,000 Israeli troops and hundreds of tanks massed on the border with Gaza.
The government has also announced the urgent call-up of "tens of thousands" of extra military reservists.
Just before the ground offensive began, Hamas issued a statement promising that Palestinian children would be picking over the ruins of Israeli tanks and the body parts of Israeli soldiers.
The militant group's exiled political leader, Khaled Meshaal, earlier warned Israel against a ground offensive, saying that a "black destiny" awaited Israeli forces if the entered Gaza.
A spokesman for Palestinian President Mahmoud Abbas condemned the offensive as "a vicious aggression".
Our correspondent says this promises to be a very bloody encounter.
'Alarm and dismay'
The UN session was convened a few hours after Israeli forces entered Gaza.
Talks lasted more than three hours and afterwards the Security Council's current president - France's Jean-Maurice Ripert - said there was a "general convergence" among some members, but he would not elaborate.
UN fails to reach Gaza consensus
The UK ambassador to the UN, Sir John Sawers, said members had got close to an agreement. He added it was disappointing there could not be a firm statement from the UN as the situation on the ground escalates.
France has strongly criticised the Israeli land campaign. The British Foreign Secretary, David Miliband, said the escalation of the conflict would cause alarm and dismay.
The US said it had told Israel's government that military action must be "mindful of the potential consequences to civilians."
The State Department also said Washington is "deeply concerned about the humanitarian situation" in Gaza, but said in a statement that Hamas holds the people of Gaza hostage.
Israeli warplanes and naval vessels have carried out more than 800 strikes on the Gaza Strip since the offensive started eight days ago, including 40 on Saturday.
The UN has warned of a worsening humanitarian crisis, and believes 25% of more than 400 Palestinians killed by Israel so far were civilians. Israel says about 80% of those killed were Hamas militants. Four Israelis have been killed by rocket fire from Gaza.
Earlier on Saturday, at least 13 people were killed in one Israeli raid when a missile struck a crowded mosque in Beit Lahiya, Palestinian medics said.
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