The clashes on Saturday began when dozens of Fatah supporters at Al-Azhar University, a strongly pro-Fatah institution, climbed on to the roof of a building, unfurled the party's yellow flag and began throwing rocks on students at the Islamic University, next door.
The Islamist students, supporters of Hamas, stoned them back.
At least 15 people were injured in the clashes.
The clashes came amidst escalating tensions between Hamas and the Fatah party of Mahmoud Abbas, the Palestinian president.
Fatah accused Khalid Mishaal, the Hamas supreme, of being hysterical for saying on Friday, in a thinly veiled reference to Abbas, that he was part of a plot to undermine Hamas and remove it from power.
"We view Khalid Mishaal's speech with concern," a Fatah statement said, referring to an address to an enthusiastic crowd of supporters in a Palestinian refugee camp in a Damascus suburb.
"We can only describe this speech as divisive, because it aims to provoke tensions in the Palestinian territories and spark civil war."
"We view Khalid Mishaal's speech with concern"
War of words
The war of words began when Abbas vetoed a Hamas government decision to create a new special force of armed militants headed by a wanted resistance fighter.
The move, the first time Abbas has revoked decisions of the new Hamas-led government, followed US criticism of the security appointment and Israeli threats to target the fighter in question.
In response, Mishaal told his audience: "What is happening in Palestine is a policy carried out by a parallel government, a counter-government which deprives us of our prerogatives and the people of their rights. It is a plot.
"A certain part of our people is plotting against us. They are carrying out a premeditated plan which is aimed at our undoing."
In its harsh response, Fatah said the speech was by "a man whose ambition is and always has been to cause Palestinian blood to flow ... while he lives in (Damascus exile) and benefits from the experiences of certain people to provoke divisions and civil wars."
"A certain part of our people is plotting against us. They are carrying out a premeditated plan which is aimed at our undoing"
It described Mishaal's remarks as "hysterical", and the speech as "full of plots, calumnies, lies and deception".
Since Friday night, pro-Abbas groups have been demonstrating in both the Gaza Strip and the West Bank.
Around 500 supporters marched in the West Bank city of Ramallah, shouting: "Long live President Abbas" and "Khaled Mishaal wants to start a civil war".
In Nablus, demonstrators shouted: "Mishaal has sold out to Syria and Iran," while others temporarily occupied the courthouse and demanded an apology.
Abbas and Hamas have been sharing power uneasily since Mishaal's group won an upset victory in January general elections, unseating Fatah and ending its grip on power of more than a decade.
On Thursday, Said Siyam, the Hamas-appointed interior minister, said he was creating a new special security force of gunmen from armed factions to supplement the work of Palestinian police and security forces in clamping down on rampant chaos in the territories.
Jamal Abu Samhadana is wanted
in Israel for scores of attacks
He nominated Gaza-based Jamal Abu Samhadana, who is wanted in Israel for scores of attacks, to a senior position in the interior ministry to oversee various security elements, including the new force.
A Palestinian official said Abbas had drawn up a decree to reverse the decisions and that it had been approved by the executive committee of the Palestine Liberation Organisation on Friday.