A civilian has been killed and three other people wounded in an exchange of gunfire near the Palestinian parliament.
The clashes were between a new Hamas-led security force, regular police loyal to the Palestinian president and unidentified gunmen, according to medics.
Witnesses say members of the new Hamas force returned fire after coming under attack from unknown gunmen.
Bystanders fled the streets.
Hamas, which took power in March after its January election win, deployed its 3,000-strong force in Gaza last week, prompting Mahmoud Abbas to order police on to the streets too. Within a day the two forces started clashing.
Overnight unidentified gunmen killed a militant from Abbas’s Fatah movement, and there were apparent assassination attempts on two leading Abbas commanders over the weekend.
This violence is fuelling concern that the situation in the Palestinian territories could descend into civil war.