Israeli forces have cut the territory in half and were ringing Gaza City itself, Palestinian witnesses said.
Soldiers and fighters were also locked in gunbattles east of the Hamas stronghold of Zeitoun.
Al Jazeera's Ayman Mohyeldin, reporting from Gaza City said: "Perhaps the most significant military development on the ground is that Gaza has now actually been split into two.
"A column of Israeli tanks and artillery, and armoured personnel vehicles has made its way through from the eastern part of Gaza, reaching as far as the Mediterrannean sea on the Western part, essentially splitting Gaza.
"That area, mostly in the former settlement of Nitzerim, it was an open area after Israel withdrew the settlement, so they were able to make strong advances all the way across Gaza, essentially cutting off the northern part from the southern part."
Witnesses in eastern Gaza tell Al Jazeera that soldiers have begun house to house operations, moving from building to building. They have also taken positions on top of many of the rooftops in that area.
Al Jazeera's Jacky Rowland, reporting from the Israeli side of the border said the authorities there have been extremely tight-lipped about the operation.
However, the military has confirmed that at least 30 soldiers have been wounded in the fight so far, two of them seriously.
Al Aqsa TV, the station affiliated to Hamas, said the group has captured two Israeli soldiers. This has not been independently verified nor has the Israeli military confirmed it.
"As far as we know, this is not true," a senior army official told reporters.
In initial clashes, Israeli ground forces killed eight Gazans, five of them fighters.
Four Palestinians were killed when a house was struck by an Israeli missile in Rafah, medics and residents said.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza City, said that the scene in Gaza was one of "fear and terror".
Palestinian medical sources say at least 477 Palestinians have died and more than 2,300 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 Sunday, from six nautical miles to 20 nautical miles, preventing humanitarian aid and protest vessels from trying to break the siege.
Around 9,000 military reservists have also been called up to assist in the ground assault.
News of the ground offensive came as the Security Council was meeting on Saturday night in New York to discuss the crisis.
Despite urgings from Libya, the only Arab nation currently on the 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.
|At least 11 people died in a raid which
hit a mosque in Gaza [AFP]
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 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.
An Israeli strike on a northern Gaza town killed at least 11 people, including one child, when a mosque was bombed.
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".
|The Israeli defence minister said Israel
had weighed all options before the raids [AFP]
"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 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.