Six Palestinians are now dead, including a 12-year-old girl, after elite troops backed by heavy armour stormed the camp overnight.
At least 50 people have so far been wounded.
Fighting erupted as Israel sent dozens of tanks into the Rafah refugee camp early on Friday on a mission, it said, aimed at destroying tunnels Palestinians used to smuggle weapons.
According to Palestinian security officials, among the dead is 23-year-old Muhammad Abd al-Wahaba, a member of Hamas' armed wing.
He was killed when an Israeli Appache fired missiles in the Ybna district demolishing two homes.
The fighting also claimed the life of Nader Abu Taha, a member of Fatah’s military wing al-Aqsa Martyrs Brigades.
Included in the wounded are two women, hit while they were in their homes, and a child injured in the back.
The condition of the women is said to be serious.
Witnesses said tanks and other armoured vehicles entered Rafah from two directions.
An 8-year-old boy and 12-year-
old girl are among the dead
They were joined by special forces, including engineering units with dogs trained to uncover tunnels. A gunbattle erupted between soldiers and Palestinian fighters.
Residents said the Israelis destroyed three houses near the border and fired machine guns to drive families away from others.
Palestinian medics said over 50 people were wounded, including six hit by rockets fired from Israeli helicopters.
An Israeli army spokesman said a soldier was slightly wounded in the eye by shrapnel from an explosive.
The Israeli general said the raid would go on "for as long as we need to find and liquidate the tunnels," some of which he said were used to smuggle weapons into Israel to attack civilians.
But after more than seven hours fighting, none of an estimated dozen tunnels being sought had been located, an officer in the field told Reuters.
Israel has mounted dozens of invasions during the conflict, including several in recent weeks, turning the Rafah refugee camp into a battlefield.
On Thursday Israel's Defence Minister Shaul Mofaz ordered a special call-up of four reserve battalions, roughly 1000 soldiers, to patrol Palestinian areas.
The call-up followed the earlier deployment of two battalions of soldiers to the West Bank and Gaza. Israel also cancelled leave and training courses and ordered the continuation of a strict lockdown preventing Palestinians from travelling within the Palestinian territories.
Aides said Palestinian President Yasir Arafat received reports about the Rafah invasion and went to bed at 02:30am on Friday (00:30 GMT). They denied rumours that he was seriously ill.
Meanwhile, in the West Bank, Palestinian politics were in turmoil after the legislature on Thursday failed to vote approval of the emergency Cabinet appointed by Yasir Arafat, leading new Prime Minister Ahmad Quraya to indicate he no longer wants the job.
Arafat may lose another prime minister
In a heated closed-door meeting at Arafat's headquarters in the West Bank town of Ram Allah, Quraya suggested he no longer wanted to be prime minister, just four days after taking office, officials said.
His predecessor, Mahmud Abbas, left office blaming the lack of support from Israel, and after losing a power struggle with Arafat.
Violence continued on Thursday in the West Bank when a human bomber detonated explosives at an Israeli army base, killing himself and injuring two Israeli soldiers and a Palestinian.
Al-Aqsa Martyrs' Brigades claimed responsibility for the attack and identified the bomber as Ahmad Safadi, an 18-year-old high school student from the village of Oref south of Nablus. It had earlier been thought that the attacker was a female.
Restrictions barring Palestinians from entering Israel and preventing many from leaving their towns have been tight since an Islamic Jihad bomber blew up a restaurant in the port city of Haifa on Saturday.
On Thursday, a woman wounded in the attack died in a Haifa hospital, bringing the toll to 20, hospital officials said.