At one point, Hamas gunmen holed up in an abandoned building hurled grenades and fired a rocket-propelled grenade at police. Other militants took up positions behind trees, cars and buildings, turning downtown Gaza into a battle zone.
Monday's battle was the most intense in an increasingly bloody confrontation between gunmen loyal to the Hamas government and the Palestinian security forces allied with moderate Palestinian President Mahmoud Abbas. The Hamas government deployed a 3,000-strong force of militants last week, sending tensions soaring.
The man killed Monday was identified as 45-year-old Khaled Radaida, the driver of the Jordanian ambassador in Gaza. Three bullets hit the windshield of Radaida's vehicle, marked with Jordanian diplomatic license plates.
Witnesses said Radaida was driving when he was hit. The ambassador, Yehiya Qarallah, was not in the car at the time.
Under police escort, the ambassador was taken to the morgue of Gaza City's Shifa Hospital and identified the driver. The diplomat sobbed as he emerged from the morgue.
Radaida's death brought to eight the number of people killed in internal fighting in Gaza this month.
Hamas and Palestinian security forces gave conflicting accounts of how Monday's fighting started, the AP reports.
The Preventive Security Service, a branch loyal to Abbas, said Hamas militiamen stopped one of its vehicles in the street and fired at the car. Hamas said some of its members came under fire during a patrol and sought cover in the abandoned building, then fired back.
During the fighting, Hamas gunmen closed main junctions and with raised weapons ordered drivers to turn back. The militiamen closed a large area between the parliament building and Palestinian police headquarters.
Abbas' Fatah movement, defeated by Hamas in January parliament elections, held Hamas responsible for the death of the Jordanian driver. Maher Maqdad, a Fatah spokesman in Gaza, said the Hamas militia is illegal and had no business patrolling near the police headquarters Monday. "When are they (Hamas leaders) going to realize that this unit is illegal and when are they going to dismantle it?" Maqdad said in a text message sent to reporters.
A Hamas spokesman, Sami Abu Zuhri, alleged that the fighting was triggered by what he called "suspicious figures" who he said opened fire on Hamas and police to stir trouble.
Earlier Monday, a gunmen linked to Abbas' Fatah movement was killed in fighting with Hamas near the southern Gaza town of Khan Younis. Fatah said two of its fighters were ambushed in their car, while Hamas said the firefight was triggered by Fatah's attempt to kidnap a Hamas member. A second Fatah gunman was wounded, the AP reports.
Tempers were also running high after two assassination attempts against security chiefs loyal to moderate Palestinian President Mahmoud Abbas over the weekend.
On Sunday, police found a 70-kilo (154-pound) bomb on the road used by Rashid Abu Shbak, a commander recently appointed by Abbas to keep Hamas-controlled troops in check. On Saturday, a bomb planted in the elevator shaft of the Palestinian intelligence headquarters seriously wounded the Palestinian intelligence chief.
Fatah officials hinted they believed Hamas was behind both incidents but stopped short of making an open accusation against Hamas.
Abbas, also the Fatah leader, called on both sides to avoid violence and said he would open talks with Hamas later this week to end the dangerous power struggle.