One of them belonged to the Popular Front for the Liberation of Palestine (PFLP) and the other to Fatah.
Palestinian sources named the PFLP activist as Ghassan Abu Khayran, 30, and said he had been wanted by Israel for the past three years. The other fighter’s identity was not immediately known.
Bethlehem is one of the few places in the occupied West Bank from which the Israeli army had withdrawn, handing it over to the Palestinian Authority last July.
In central Gaza, two Palestinian fighters were killed in clashes with Israeli soldiers near Kisovim settlement, east of Dair al-Balah city, our correspondent in Gaza reported, quoting Palestinian sources.
The resistance groups Al-Aqsa Martyrs Brigades and al-Quds Brigades issued a mutual statement claiming responsibility for the Kisovim operation, added our correspondent.
The fighters were named as Muwafaq Al-Aaraj, 22, of the Islamic Jihad and Muhannad Abu Hatab belonging to an armed offshoot of Palestinian leader Yasir Arafat’s Fatah movement, Al-Aqsa Martyrs Brigades.
Meanwhile, several Israeli soldiers were wounded in the southern West Bank town of Hebron on Friday, it what medics said could have been a “friendly fire” incident. The troops may have been hit by gunfire from other Israeli soldiers, medics said.
Palestinian witnesses said at least three soldiers were evacuated by ambulance.
Two Israeli soldiers were also injured on Friday noon when an explosive device hit their patrol as it was heading towards Netzarim settlement in south Gaza city, our correspondent reported.