Israeli troops and tanks cut swaths through the Gaza Strip early Sunday, surrounding its biggest city and effectively cutting the territory in two as the offensive against Hamas gained momentum.

Israeli infantry soldiers enter the Gaza Strip from Israel on Sunday. (Sebastian Scheiner/Associated Press)

Doctors in Gaza say 64 Palestinians have been killed since the ground offensive began after nightfall Saturday. At least four of the dead were Hamas fighters and the others were civilians.

Heavy gunfire was reported in Gaza on the second day of Israel's ground assault and the ninth day of its air attacks against Hamas targets.

Witnesses reported clashes between Israeli soldiers and Palestinian fighters around towns north and south of Gaza City. They include Beit Hanoun, Beit Lahiya and Jebaliya refugee camp. Israeli troops were also spotted in the Zeitoun area south of Gaza City.

Israeli officials have predicted a long and difficult campaign to try to stop Hamas fighters from firing rockets into southern Israel.

Israel's ground offensive condemned

Condemnation of Israel's ground operation poured in from the Middle East and Europe.

"The violence has to stop," said European Union External Relations Commissioner Benita Ferrero-Waldner.

U.S. officials maintained their firm support for Israel and squarely blamed Hamas.

Canadian Foreign Affairs Minister Lawrence Cannon said in a statement, "Canada is deeply concerned about the increase in hostilities between Israel and Hamas."

"We urge renewed international diplomatic efforts to achieve a sustainable and durable ceasefire, starting with the halting of all rocket attacks on Israel. Canada maintains that the rocket attacks are the cause of this crisis," he said.

Cannon also urged the international community to come together to address the humanitarian situation, including ensuring access to food, fuel and medical supplies.

More than 5,000 people held anti-Israel rallies in Istanbul and thousands more gathered in Beirut on Sunday.

In Canada, thousands gathered Sunday in Montreal and about 300 in Edmonton, urging the Canadian government to apply pressure on Israel to stop its military offensive.

Similar protests were held Saturday in Ottawa, Toronto and Vancouver as well as in Paris, London and Amsterdam.

Over 500 Palestinians killed

The latest deaths brought the toll in the Gaza Strip since Israel launched its air campaign Dec. 27 to 512. Palestinian and UN officials say at least 100 civilians are among the dead.

Army ambulances were seen bringing Israeli wounded to a hospital in the southern Israeli city of Beersheba. The military reported 40 Israeli troops were wounded, two seriously.

In his first public comments since the ground operation was launched, Israeli Prime Minister Ehud Olmert told his cabinet on Sunday that Israel could not allow its civilians to continue to be targeted by rockets from Gaza.

Palestinian residents of east Jerusalem participate in a protest outside Damascus Gate in Jerusalem's Old City on Sunday against Israel's military operation in Gaza. (Dan Balilty/Associated Press)

"This morning I can look every one of you in the eyes and say the government did everything before deciding to go ahead with the operation," he said.

A senior Israeli military officer said Hamas seemed well prepared for the invasion of Gaza, a densely populated territory of 1.5 million where militants operate and easily hide in the crowded urban landscape.

He said the operation was "not a rapid one that would end in hours or a few days."

Still, the officer said, "We have no intention of staying in the Gaza Strip for the long term." He spoke on condition of anonymity in accordance with army regulations.

Israel says the objective is to restore quiet to Israel's south, not to topple Hamas or reoccupy Gaza.

Defending Israel's decision to attack, Israeli President Shimon Peres told ABC News This Week, "We don't intend neither to occupy Gaza nor to crush Hamas, but to crush terror. And Hamas needs a real and serious lesson. They are now getting it."

A spokesman for Hamas, Ismail Radwan, promised his fighters would turn Gaza into a "graveyard" for Israeli forces.