Hundreds of Palestinians have rallied outside parliament in Gaza City, urging rival factions to stop violence and restart unity government talks.
The Fatah group agreed to maintain the truce, despite two deaths
The demonstration came a day after two members of the Fatah movement of President Mahmoud Abbas were killed in Gaza City, despite a formal ceasefire.
Early on Friday, fierce gun-battles erupted in Gaza City between Hamas supporters and members of a local clan.
In Ramallah, Mr Abbas again urged all parties to respect the truce.
He said he was still open to the idea of forming a national unity government, despite his call for early elections.
However, his spokesman said there had been no preparations for any new round of talks.
Friday's clashes happened near the home of the Hamas foreign minister, Mahmoud al-Zahar.
Unconfirmed reports say at least one person was killed and at least one member of Hamas abducted.
9 Dec - Mr Abbas suggests early polls; Hamas denounces the idea
11 Dec - Three sons of a Fatah security chief are shot dead on their way to school
14 Dec - Hamas PM Ismail Haniya's convoy comes under fire as he returns from Egypt, killing a bodyguard; Hamas blames Fatah
16 Dec - Mr Abbas says he will call early elections; Hamas calls the move a "coup"
17 Dec - A truce is called after street battles between Hamas and Fatah, but violence continues
19 Dec - Formal truce signed, troops begin leaving streets
Mediators intervened to help end the fighting, which came two days into a truce between political rivals Fatah and Hamas.
Both factions withdrew their troops from Gaza's streets on Wednesday morning, on the first full day of a formal ceasefire.
The truce followed serious clashes between the two Palestinian factions, sparked by President Mahmoud Abbas's call for early elections.
Two Fatah policemen were killed hours into the ceasefire, but the group said it would maintain the truce.
Relations between Fatah and Hamas have been poor since Hamas won a shock election victory in January ousting Fatah from power.
But a Western aid boycott imposed because of Hamas' refusal to recognise Israel or renounce violence has helped create a political deadlock.
The groups negotiated over forming a government of national unity but failed to agree terms.
Last week bitterness spilled over into violence, with apparent assassination attempts against Mr Haniya and Foreign Minister Mahmoud Zahar.
Mr Abbas' call for fresh elections sparked more fighting before the ceasefire was agreed.