Israeli troops have clashed with Palestinian militants on the edge of Gaza City on the third night of Israel's ground assault on Gaza.
The Hamas and Islamic Jihad groups say fighters engaged Israeli soldiers with machine-guns and rocket fire.
Three Israeli soldiers were also killed by "friendly fire" in northern Gaza.
Some 540 Palestinians are thought to have been killed and 2,500 wounded in the 10 days since Israel moved to end rocket attacks from within Gaza.
Palestinian medical officials say at least 90 people have died since the ground assault began while Israel has lost four soldiers and four civilians over the 10 days.
Aid agencies in Gaza speak of appalling conditions for treating casualties of the continuing Israeli bombardments.
Eyewitnesses reported that Israeli tanks had for the first time moved into the southern city of Khan Younis.
Rejecting international appeals for a ceasefire, Israeli Defence Minister Ehud Barak said on Monday that the operation would continue until it met its objective.
Foreign diplomatic efforts to resolve the crisis have borne little fruit so far.
An Israeli army spokesman said three soldiers from the elite Golani Brigade had been killed accidentally by a single tank shell, with a further four severely wounded and 20 suffering lighter injuries.
Israel says the operation will continue until it reaches its objectives
"In the fierce battle that was being waged between our Golani brigade soldiers against the Hamas... unfortunately one of our tanks actually exploded on to a building where our forces were located," Capt Guy Stiegelman told the BBC.
At nightfall on Monday, Israeli troops were reported to be battling Palestinian militants on the outskirts of the Shujaiya district of Gaza City.
Hamas and Islamic Jihad said their fighters had engaged Israeli soldiers with machine-guns and rockets. Residents reported hearing loud explosions and heavy gunfire.
Israel's Haaretz newspaper, quoting Israeli army sources, reports that Hamas lobbed mortars at the soldiers.
Artillery and helicopter gunships were reportedly brought in to drive back the Palestinian fighters.
Describing fighters' tactics, an unnamed Hamas official told AFP news agency that fighters had lured Israeli forces into a trap.
"We have left a lot of explosives in their path," he added.
Islamic Jihad spokesman Abu Ahmed said the group had lost one man in the fighting in Shujaiya.
"Communications with our fighters are cut at the moment but it [combat] is still going on," he added.
Israeli tanks were also reportedly moving towards the Bureij refugee camp in central Gaza and Beit Hanoun and the Jabaliya refugee camp saw clashes on Monday.
Information about what is happening inside Gaza is limited as Israel has barred foreign reporters from entering.
Living conditions in Gaza are reported to be deteriorating sharply, with supplies of fuel, food, water and wheat running desperately low.
Norwegian doctor Mads Gilbert, one of two foreign doctors working at Gaza's biggest hospital, al-Shifa, said operating rooms were full and people were dying because of a lack of supplies.
Israel says it is not targeting civilians but Dr Gilbert said he had only seen two fighters among hundreds of casualties.
The UN says a million people in the territory are without electricity and many are facing "serious hunger" within days.
Dominic Nutt, of the aid agency Save The Children, told the BBC that workers in the territory were reporting rapidly deteriorating conditions:
"They don't have any water most of the day, there is no electricity, they are freezing cold, the windows have to be left open to stop them smashing when the bombs fall.
"Children are at risk from hypothermia, they are malnourished, there is not enough food, the situation is getting desperate."
Thousands of Gazans are reported to have fled their homes, despite the dangers of moving around outdoors in the territory.
Israel says it has allowed a convoy of 80 lorries carrying food and medicines through Gaza's southern border with Egypt.
French President Nicolas Sarkozy is to travel to Damascus on Tuesday along with an EU delegation in a bid to persuade Syria to influence Hamas leaders to accept his plan for a ceasefire.
He held talks with Israeli and Palestinian leaders in the region on Monday.
Accusing Hamas of acting in an "irresponsible and unforgivable manner" by firing rockets into Israel, he appealed to Israel for a halt to the violence to allow in humanitarian aid.
Palestinian President Mahmoud Abbas is due to attend a UN Security Council meeting on Tuesday, along with the foreign ministers of Saudi Arabia, Egypt, France and Britain, in an attempt to put pressure on the Security Council to act decisively.
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