Friday's truce was agreed after Khalid Meshaal, head of Hamas, and Mahmoud Abbas, head of Fatah, agreed during a phone conversation to attempt another ceasefire and to withdraw their gunmen from the streets, a senior Fatah leader said.
But the current ceasefire, the second announced in a week, appeared to be having little effect.
Khalid al-Batsh, an Islamic Jihad leader, said in an interview with Al Jazeera: "A joint bureau of Hamas, Fatah, Islamic Jihad, the Popular Front for the Liberation of Palestine [PFLP] and the Democratic Front for the Liberation of Palestine [DFLP] will resume meetings to ensure continuity of the ceasefire."
"We are now holding intensive contacts with all factions ... Egyptian mediation efforts have also continued to try to resolve the crisis.
"Gunmen in the street"
Officials were due to meet later on Saturday to hammer out a fuller deal, but neither side had so far implemented Friday's agreement to rein in their armed forces and dismantle checkpoints erected across the Gaza Strip.
Abu Amr, a 40-year-old citizen of Gaza, described the ceasefire agreements as "a joke and a broken record".
He said he was keeping his three children at home even if schools re-opened.
"I will not send them until I am sure that there are no gunmen in the street and we stop hearing the sounds of bullets and explosions," he said.
Fatah gunmen stormed the Agriculture Ministry, ransacking offices and stealing computers and official documents, said Mohammed al-Agha, the Agriculture Minister said on Saturday.
Fatah denied anything had been stolen.
Running gun battles
Residents of the Gaza Strip had hidden in their homes on Friday as armed men fought running gun battles firing rifles and rocket-propelled grenades from streets and rooftops.