Abu Abir, a PRC spokesman, said that armed men loyal to Mohammed Dahlan, the former Preventative Security Service chief in Gaza and a Fatah member in the new Palestinian parliament, were caught spying on al-Quqa's home on Thursday.
Abu Abir promised "an open war" on Dahlan and several other security commanders.
Palestinian intelligence officials said al-Quka was a known Hamas supporter, and appeared to have been killed for his loyalties. The officials, fearing for their safety, spoke on condition of anonymity.
Dahlan, who was travelling in the UAE, dismissed the PRC's allegations as "baseless ugly accusations".
When Abu Abir called a news conference to discuss the killing, rival armed men burst on the scene and shots were fired. Hospital officials said two boys, aged 15 and 13, were wounded, one seriously.
Armed men gathered outside the hospital where al-Quqa's body was taken, crying, screaming and firing into the air. Accompanying the body, hundreds of armed men marched through Gaza City.
After the funeral, dozens of Fatah-linked armed men blocked the roads leading to Samir Masharawi, another figure close to Dahlan. A spokesman for the armed men pledged to take "all necessary measures against Abu Abir. He must be punished".
Israeli warplanes struck Gaza
after Thursday's suicide attack
Mahmoud al-Zahar, the Palestinian foreign minister, said of the Gaza explosion: "It means that the Israeli aggression will not stop. It means our resistance should continue."