Israeli troops and tanks split the Gaza Strip and ringed its main city on Sunday in an offensive against Hamas militants but civilians trapped in the Palestinian enclave suffered more bloodshed.

Israeli tanks poured shells and machinegun-fire into suspected militant positions and war planes struck from the skies as Hamas fighters fought back with mortars and rockets.

Hamas rocket salvoes also hit southern Israel, strengthening Israel's resolve to stamp out the threat which the Jewish state says made its offensive necessary.

The Saturday night invasion of Hamas-ruled Gaza followed a week of Israeli bombardments from land, sea and air -- the most serious fighting in decades in the Israel-Palestinian conflict.

At least 34 Palestinians, most of them civilians, were killed on Sunday as Israeli shells slammed into houses and Gaza's main shopping district, medical sources said. That brought the death toll to more than 500 in Gaza in the nine days of Operation Cast Lead.

Four Israelis have been killed by the Hamas rocket strikes since December 27 and 32 Israeli soldiers wounded in the ground offensive, Israel said.

Israeli officials said the offensive, whose stated aim is to wreck the militants' rocket-launching infrastructure, could last many days.

The government did everything before deciding to launch the operation. This is an unavoidable operation, Israeli Prime Minister Ehud Olmert said.

Calls for a ceasefire from the United States, Israel's main backer, other foreign governments and the United Nations failed to gain traction over disagreements about who should stop shooting first.

TERRITORY CUT IN HALF

Israel has barred foreign correspondents from entering Gaza.

But Palestinian witnesses said the Israeli thrust cut Gaza in half from the border fence to the Mediterranean shore. Troops and armor had taken up siege positions around Gaza City itself.

Sunday morning saw gun battles between Hamas fighters and Israeli soldiers but later the action was mostly Israeli tank shelling and Hamas rocket and mortar-fire.

I would say that most of the resistances that we faced were from mortar shells and other things but not from serious Hamas fighters face-to-face, an Israeli officer said in Jerusalem.

Israeli aircraft struck dozens of targets, including arms- smuggling tunnels, weapons caches and mortar squads. Dozens of Hamas fighters were hit, the Israeli military said, without being more specific.

Among the Palestinian casualties were five civilians killed and 40 wounded when tank shells slammed into Gaza City's main shopping area. Two children were dismembered by another blast from a tank, medical workers said.

A foreign Red Crescent doctor said: Civilians are being killed ... shells are severing people's legs, shrapnel is going into people's bodies and into people's homes, a lot of people are being cut down. Everyone is terrified.

Heavy civilian casualties in the territory packed with 1.5 million people could increase international pressure on Israel to halt its biggest operation in Gaza in four decades.

But the fighting also holds political risks for Israeli leaders before a February 10 national election, especially if its forces take heavy casualties in street fighting.

A spokesman for Hamas's armed wing, the Izz el-Deen al-Qassam Brigades, said Israeli troops faced death or capture.

The Zionist enemy must know his battle in Gaza is a losing one, spokesman Abu Ubaida said.

The Iranian-backed Hamas, which sees itself as the forefront of Palestinian resistance to Israel but is considered a terrorist group by Israel, the United Sates and the European Union, is estimated to have about 25,000 fighters.

They are believed to have laid landmines and booby traps to hinder the Israeli advance.

Israel has not disclosed how many troops are involved in the operation but thousands of reservist have been put on stand-by in an indication of the scale of the mobilization.

In southern Israeli towns, residents hoped the offensive would bring a reprieve from the Hamas rockets but schools and malls remained closed and many streets were eerily empty.

About 25 rockets were fired on Israel on Sunday, one hitting a house in Sderot and wounding a woman, the army said.

The plight of Gaza residents was desperate. People have taken shelter in their homes for days and humanitarian agencies warned that water, food and medical supplies were running short.

DIPLOMATIC MOVES

The United States said a ceasefire should take place as soon as possible but must guarantee an end to Hamas rocket strikes.

Former British Prime Minister Tony Blair, envoy for powers sponsoring Middle East peace talks, was to meet Israeli Defense Minister Ehud Barak on Sunday. French President Nicolas Sarkozy is due in Jerusalem on Monday.

U.N. Secretary-General Ban Ki-moon called for an immediate end to the ground operation. In a telephone conversation with Olmert, Ban conveyed his extreme concerns and disappointment, a U.N. statement said.

Hamas called off a six-month truce with Israel last month and stepped up its rocket attacks, complaining at Israeli raids into Gaza and a continuing blockade of the enclave which Israel occupied from 1967 to 2005.

International peace efforts aimed at creating an independent Palestinian state foundered after Hamas won elections in 2006 and drove Fatah forces loyal to Palestinian President Mahmoud Abbas from Gaza a year later.

Israel