Hamas and a group known as the Fatah Hawks, from the dominant Palestinian faction, said they carried out Sunday’s attack.
The Fatah group said it was avenging the assassination of Yasir Arafat, referring to rumours widespread among Palestinians that their veteran leader was poisoned.
French and Palestinian officials have denied the rumours.
The groups said they burrowed 600 metres to reach the Israeli post at the Rafah border before detonating a 1500kg bomb.
They said they opened fire and later set off another large blast nearby.
Israeli media said two Palestinian bombers were believed to have died in the first explosion.
At least eight wounded people were being treated by medics and would be evacuated to hospital by military helicopters, radio stations said.
Ariel Sharon plans to pull Israeli
The army has not commented on Aljazeera’s report about Israeli fatalities.
But within hours, Israeli helicopter gunships fired about six missiles at various buildings in Gaza City.
No occupation forces spokesperson has named the identities of the targets, but residents said the city was being pounded in numerous locations.
Israel has vowed to respond to violence, but said it could cut back on military operations if resistance groups waging an uprising against occupation stop attacks on Israelis.
Sharon wants to evacuate all Israel’s illegal settlements in the Gaza Strip and four of 120 in the West Bank next year in a bid to “disengage” from fighting with the Palestinians.
Polls show most Israelis want to part with impoverished Gaza.