Sporadic gun battles are continuing in Gaza between the rival Hamas and Fatah factions, despite a renewed truce.
Clashes have broken out in two areas of Gaza City although reports say the fighting has been intermittent.
Twenty-two people were killed and at least 200 wounded in 24 hours before the truce was revived on Friday.
In Washington, the Quartet of Middle East mediators - the EU, the UN, the US and Russia - voiced "deep concern" about the levels of violence.
The Quartet also supported a US push to revive the stalled peace process between the Palestinians and Israel.
Tense time
The BBC's Gaza correspondent, Alan Johnston, says residents of Gaza City woke up on Saturday to the sound of more gunfire.
However, neither party launched major assaults during the night, he adds, and there remains a sense that the wider situation has improved.
The recent clashes between Hamas and Fatah were the most intense seen during months of factional unrest in Gaza.
On Friday leaders of both sides promised to withdraw their fighters and remove their checkpoints, but this has not yet happened and there remains a danger of further fighting, our correspondent says.
Hamas and Fatah leaders are due to meet later on Saturday to try and shore up the truce.
And reports say Palestinian Authority President and Fatah chief Mahmoud Abbas and Hamas political chief Khaled Meshaal will meet in Saudi Arabia next Tuesday to try to end the fighting.
Hamas and Fatah have been trying to form a unity government for months.
They are deadlocked over Hamas' rejection of international calls for it to recognize Israel.
Western donors have been withholding direct aid, resulting in a deep economic crisis in the Palestinian territories.
Quartet talks
In Washington, the Quartet of Middle East mediators "called for Palestinian unity in support of a government committed to non-violence, the recognition of Israel and acceptance of previous agreements," UN Secretary General Ban Ki-moon said on behalf of the group.
The Quartet re-affirmed that a year-long aid embargo against the Hamas government would remain in place until it agrees to recognize the Jewish state and renounce violence.
But Russian Foreign Minister Sergei Lavrov described the boycott as "counterproductive".
He also advocated bringing Syria into the Middle East peace dialogue - a suggestion ruled out by US Secretary of State Condoleezza Rice.
The Quartet also backed US efforts to jump-start the so-called "roadmap" for a peaceful settlement between the Palestinians and Israel.
Three-way talks between Ms Rice, Mr Abbas and Israeli Prime Minister Ehud Olmert are expected to be held later this month.
Photo caption
Hamas fighter in Gaza