Several men hurled sticks, flags and rocks at each other, according to reports.
At least nine people were injured, including an Agence France Presse photographer.
Sunday's incident happened as Palestinian leader Mahmud Abbas told Israel TV that he hoped for a truce declaration by all Palestinian factions at a meeting in Cairo this week.
Tension between Fatah and Hamas has been a major factor in Palestinian politics over the past decade.
Hamas announced officially on Saturday that it will field candidates in a parliamentary election. The election is set for July, only the second since the Palestinian Authority was created in 1994.
Hamas boycotted the 1996 vote, refusing to recognise the interim Palestinian-Israeli peace accords that set up the legislature.
For Hamas, this is the first foray into election politics, having made its name up to now with welfare programmes for destitute Palestinians and dozens of bomb attacks in Israel.
Because of widespread voter dissatisfaction with corruption and inefficiency, Fatah stands to take a beating at the polls, with Hamas as a main beneficiary.