Ayman Mohyeldin, Al Jazeera's correspondent in Gaza City, said that the scene in Gaza was one of "fear and terror".
He said that there were reports of heavy fighting between Israeli forces and Palestinian fighters in areas such as Zaytoun, near Gaza City, as several loud explosions rocked the territory.
Palestinian medical sources say at least 464 Palestinians have died and more than 2,000 had been injured since Israel began aerial bombardment of Gaza more than a week ago.
Four Israelis have also been killed by Palestinian rockets fired into southern Israel during the past week.
Israel, meanwhile, extended its naval blockade of Gaza early on Suday, from six nautical miles to 20 nautical miles, preventing humanitarian aid and protest vessels from trying to break the siege.
News of Israel's new ground offensive came as the United Nations Security Council was meeting on Saturday in New York night to discuss the crisis.
Despite urgings from Libya, the only Arab nation currently on the security council, to issue a statement expressing "serious concern" over the offensive, the meeting adjourned without reaching any agreement.
Riyad Mansour, the Palestinian permanent observer to the UN, condemned the result, saying that "just, as they say, Israel has the right to defend itself, we the Palestinians have the right to end occupation".
"We are demanding from Israel, the occupying power and agressor, to stop this agression immediately," Mansour said.
A UN spokesman said that Ban Ki-moon, the UN secretary-general, was "deeply concerned" by the latest events.
Ban had spoken to Ehud Olmert, the Israeli prime minister, and conveyed his "extreme concern and disappointment", the UN said in a statement.
France added its voice to the discussion, condemning Israel's ground offensive on Saturday. The foreign ministry said in a statement that the "dangerous military escalation" complicated efforts to end the fighting, bring aid to civilians and reach a permanent ceasefire.
The US state department said that a Gaza ceasefire should take place as soon as possible and that it had told the Israeli government that any military action should be "mindful of the potential consequences to civilians".
It also condemned Hamas, saying it was holding the people of Gaza "hostage" and contributed to a "very bad daily life" for the coastal territory's residents.
White House officials also said that George Bush, the US president, had been briefed on the situation in Gaza and that US officials were in contact with authorities "in the region" and in Europe.
Mahmoud Abbas, the Palestinian president, and several Arab foreign ministers were flying to New York over the weekend to urge the UN security council to again try to adopt an Arab draft resolution that would condemn Israel and urge a halt to the Gaza offensive.
The ground attacks followed a salvo of air raids in Gaza on Saturday.
|At least 11 people died in a raid which
hit a mosque in Gaza [AFP]
An Israeli strike on a northern Gaza town killed at least 11 people, including one child, when a mosque was bombed during evening prayer.
There has been no official confirmation from either side of casualties from the ground assault so far, although Zeina Awad, Al Jazeera's correspondent in Jerusalem, said Israeli media was reporting that several Hamas fighters had been killed at the start of the ground offensive.
The Reuters news agency also quoted a senior Hamas official as saying that Palestinian fighters had killed a number of Israeli soldiers.
Ehud Barak, Israel's defence minister, said on Saturday that the operation was aimed at forcing Hamas "to stop its hostile activities against Israel and bring about significant change".
"We have carefully weighed all our options, we are not war hungry but we should not allow a situation where our towns are constantly targeted by Hamas," he said.
Mark Regev, an Israeli government spokesman, later told Al Jazeera that the "single aim" of the offensive was to halt Hamas rocket attacks into Israeli territory.
"Ultimately Hamas is solely responsible for this crisis and today they are paying a price for that," he said.
Hamas has vowed to defeat the Israeli army following the invasion, with Osama Hamdan, a senior official for Hamas in Beirut, Lebanon, telling Al Jazeera that "military operations will not win for the Israelis".
On Friday, Khaled Meshaal, the political leader of Hamas, had warned that any Israeli ground offensive would lead to a "black destiny".
Al Jazeera's Ayman Mohyeldin reports that power lines have been cut throughout the Gaza Strip and more than 250,000 people in the northern part of the territory are without electricity.
|The Israeli defence minister said Israel
had weighed all options before the raids [AFP]
"The biggest concern is a ground invasion could result in urban warfare," he said.
"Rockets are being fired from deeper and deeper within Gaza and if Israel's intention is to prevent such attacks how far into Gaza, an area densely populated with civilians, will they need to go?"
Fears of a humanitarian crisis have also grown in recent days, as the strip, home to 1.5 million people, is already suffering shortages of fuel, food and medical supplies due to a two-year economic blockade imposed by Israel.
The International Committee for the Red Cross said on Saturday its medical emergency team had been prevented for a second day from entering the territory.
The UN has warned that there were "critical gaps" in aid reaching Gaza, despite claims from Tzipi Livni, the Israeli foreign minister, that there was no crisis and that aid was getting through.
At least 25 per cent of the Palestinians killed since Israel began its aerial assault nine days ago were civilians, the UN has estimated.