Said Siam, the Palestinian interior minister, said on Sunday: "We will ensure that nobody is above the law and demand an end to the instability and armed chaos."
He was speaking in reference to violence on Friday in which 36 people were wounded after the assassination of a commander from the Popular Resistance Committees.
"We are giving the security forces all the authority and power to investigate this ugly crime and also the three killings and other casualties that followed," he said, referring to a commission of inquiry set up on Friday night.
The umbrella group of Palestinian factions, the Committee of Islamic and National Forces, also called for an end to instability and armed chaos.
It condemned the war of words between rival groups that followed the murder of Abu Youssef al-Quqa.
"We condemn the accusations being bandied about against different Palestinian groups and affirm our concern for Palestinian unity in confronting the occupation," a statement said.
"We ask the interior ministry to investigate the killing and try those responsible as well as opening investigations into other assassinations and into collaborators."
Al-Quqa was killed on Friday
The mainstream Fatah movement of Mahmoud Abbas, president of the Palestinian Authority, whose supporters clashed with members of the Popular Resistance Committees on Friday, expressed concern for Palestinian unity and worry about the bloodshed, which it described as a "red line".
"It is a red line for us. We will not allow anyone to touch it and to use it for his interest and party point of view," a statement said.
"We confirm our commitment to supporting the Palestinian Authority and imposing the rule of law and back [prime minister Ismail] Haniya's government in establishing a commission of inquiry into what happened in Gaza City."
Friday's violence was the first serious challenge faced by the Hamas-led government since its inauguration two days earlier and its landslide January election victory over Fatah.