Hamas confirmed the clash in a statement but made no mention of casualties.
The military detained dozens of Palestinians aged between 15 and 50
for questioning and identity checks, witnesses said.
On Monday, the Israeli army carried out an incursion deep into Palestinian territory, also at Rafah, in a one-day operation in which they questioned dozens of Palestinians and arrested four.
"Hamas is trying to draw us [Israel] into their civil war"
Zafon, Beersheva, Israel
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Elsewhere, four armed Palestinians attacked the Kissufim crossing checkpoint between central Gaza and Israel, Palestinian security sources said.
The Israeli military said that clashes broke out in the sector and that Palestinian fighters from Gaza infiltrated into southern Israel on Saturday during an attack on the border crossing.
A military spokesman said: "There was an infiltration into Israeli territory in the area of the Kissufim crossing."
He said the military believed it had located the fighters, but did not say how many might have got through.
A spokesman for al-Quds Brigades, the armed wing of Islamic Jihad, said two of the fighters belonged to al-Quds Brigades and two other were members of al-Aqsa Martyrs Brigades.
The fighters stormed the post in an armoured jeep, similar to those of the Israeli military, killing one soldier, the spokesman said.
Hiba Akila, Al Jazeera's correspondent in Gaza, said the joint operation, of al-Quds Brigades and al-Aqsa Martyrs Brigades, has been called "the hot summer" operation.
It was called a retaliation for Israeli practices against the Palestinians, she said.
A 17-year old Palestinian young man was also reported to have been killed and another injured by Israeli fire near the West Bank city of Hebron.
Residents of the area said that Israeli soldiers opened fire at the two young men who went hunting near the city, affirming that the two victims were not affiliated with any Palestinian faction.
The Israeli army admitted it opened fire at the two young men, claiming that the presence of armed men in the area was a threat that should be dealt with.
Meanwhile, medics at a northern Gaza Strip hospital walked off their jobs for a few hours on Saturday to protest the kidnapping and kneecapping of a doctor by Palestinian armed groups, the first physician targeted in months of deadly infighting.
Fayez al-Barrawi, a known Hamas supporter, was blindfolded, handcuffed and shot six times in the legs, including a kneecap, and then tossed on the street on Thursday. Hamas has said Fatah fighters were behind the kidnapping.
Al-Barrawi worked at Beit Hanoun hospital in the northern Gaza Strip, close to the border with Israel.
It is the first time a doctor was seized. However, fighters often fire on paramedics and ambulances during gun-battles.