The clashes erupted during an Israeli raid into the refugee camp on Friday, Aljazeera's correspondent Hasan al-Titi said.
The two Palestinians killed are Alaa al-Tirawi and Jamal al-Jirny, activists of Fatah's al-Aqsa Martyrs Brigades. A third activist of the group, Muhammad Qitawi,i was shot in the chest by Israeli fire, al-Titi said.
The resistance group, originally an offshoot of Palestinian President Mahmoud Abbas's Fatah ruling party, announced the deaths over loudspeakers before dawn on Friday in Balata refugee camp.
The Palestinian Authority on Friday condemned the ongoing Israeli escalation in the West Bank and the "crime" in Balata refugee camp in Nablus.
Chief Palestinian negotiator Saeb Erekat warned that the continuation of the Israeli aggression would lead to the collapse of the truce declared by the Palestinian factions in collaboration with the Palestinian authority.
He also called on the international community to intervene to help the Palestinian authority consolidate the truce.
Aljazeera correspondent in Nablus said the al-Aqsa Brigades have vowed to avenge the killing of two of its elements by Israeli troops and said that they would no longer commit themselves to the truce.
On Thursday, Israeli troops shot dead three Palestinians in raids in the occupied West Bank, widening a week-long offensive despite a halt to home-made rocket salvoes from Gaza that had resumed after Israel's withdrawal.
Al-Aqsa Brigades vowed to
avenge the killings
Israel has also arrested hundreds of suspected resistance members in sweeps into Palestinian villages and towns in the West Bank, where large illegal Jewish settlements remain.
The wave of violence since last Friday has badly frayed a seven-month-old ceasefire and deflated dreams in Gaza of a swift economic upswing in the battered, densely populated coastal territory after the Israeli withdrawal.
It has also chastened hopes that Israel's departure from Gaza - centrepiece of Prime Minister Ariel Sharon's plan for "disengaging" from conflict with Palestinians - would provide momentum towards renewing peace talks frozen since 2000.