A spokesman for the Popular Resistance Committees (PRC) said on Thursday that it was responsible for the attack near the Morag colony north of Rafah city.
A PRC spokesman said two of its members had also been killed during the attack but that a third survived the clash and had phoned in details of the operation.
An official at the settlement, Nissim Dehan, told Israel's Army Radio that troops had "suffered a heavy blow".
Israeli security sources confirmed that three soldiers died but refused to provide names.
Aljazeera's correspondent in Gaza said Israeli forces have begun making house-to-house searches in nearby Palestinian villages and that Apache helicopters are making continuous sweeps over the whole area.
Meanwhile, Israeli occupation forces launched a fresh raid on the Khan Yunus refugee camp in southern Gaza, injuring two.
A missile landed near a mosque in the camp, Aljazeera's correspondent said.
Israeli soldiers used loudspeakers demanding Palestinians to evacuate their houses, while many Israeli military bulldozers, backed by around 20 military vehicles, raided the area, the correspondent added.
In the name of destroying "the infrastructure of Palestinian terrorism", the army demolished seven homes and razed farm land to the ground in the al-Barabkha district of the camp, Aljazeera's correspondent said.
"An Apache helicopter also fired two missiles. The first landed in open ground, but the second hit a home and injured more than 15 Palestinians inside, some seriously," the correspondent said.
Israeli troops have blown up
Zainab Abu Salim's family home
The Israeli army explained the measures would prevent Palestinian resistance groups from targeting military sites near illegal settlements and harming Israeli citizens.
Tel Aviv plans to withdrawal from occupied Gaza next year, but many resistance groups remain suspicious that it will ever abandon its illegal settlements and so continue to wage a now four-year-old intifada.
Jenin and Nablus were also under Israeli invasions on Thursday.
Backed by more than 30 Israeli military vehicles and Apache helicopters, troops stormed into Jenin's refugee camp, Aljazeera's correspondent said.
Searching for "wanted activists" during the third raid in as many days, gunfire and explosions where heard as soon as soldiers reached the centre of the camp.
Occupation forces arrested 16 Palestinians in the West Bank cities of Hebron, Jenin, Nablus and Ram Allah.
Israeli forces have also demolished two homes in the West Bank city of Nablus.
Aljazeera's correspondent said the first house belonged to the family of Jerusalem bomber Zainab Abu Salman in the Askar refugee camp.
The other belongs to Alaa Sanakra, a wanted al-Aqsa Martyrs Brigades activist, in the Balata refugee camp.