A Palestinian police commander and two bystanders have been killed in clashes in Gaza City between security forces and Hamas militants.
The police have been asserting their control in the strip
At least 50 other people were injured in the fighting, which flared up when police tried to stop a car carrying Hamas activists in Gaza City.
Hamas said police tried to arrest the son of a former leader, but police said they were trying to resolve a dispute.
Separately, the Israeli and Palestinian leaders have agreed to hold new talks.
The BBC's Alan Johnston reports that the Gaza clashes were sporadic but, at times, intense exchanges of fire and occasionally the sound of grenade blasts echoed across the city.
Police and Hamas militants briefly exchanged gunfire in a clash on Nasser Street, which police say began when they were attacked by Hamas supporters as they tried to resolve a minor dispute.
Hamas said the police were trying to detain Mohammed al-Rantissi, son of Abdel Aziz Rantissi, the Hamas leader killed in an Israeli air strike last year.
Fighting spread to two other parts of Gaza City, with Hamas supporters attacking police stations there.
Reports say Hamas members used rifles, rocket-propelled grenades and hand grenades.
The dead police commander is reported to have held the rank of major.
Our correspondent notes that the clashes come just days after the Palestinian Authority stepped up the security forces' presence on Gaza streets.
It has been trying to enforce a ban on the carrying of weapons in public in attempt to improve the very poor law and order situation.
Palestinians shopped for food for Ramadan as the battles raged
Militant groups including Hamas have said they support the effort to counter any criminal activity, but insist on keeping their weapons for confrontation with Israel. They say the authorities must not attempt to disarm them.
"Hamas bears full responsibility for the result of these acts and the serious violation of law and order and playing with the blood of our people," the Palestinian interior ministry said in a statement on Sunday.
"We are determined to move ahead with our plans to implement law and order and we will not let anyone be above the law."
Israeli Prime Minister Ariel Sharon earlier spoke to Palestinian leader Mahmoud Abbas by telephone and agreed to meet at an unspecified date in the near future.
A meeting had been scheduled for Sunday but was postponed because of a recent Israeli offensive in the Gaza Strip, launched after militants fired rockets into Israel.
Israel has announced an end to the offensive, which included missile attacks on Gaza, the killing of a number of Palestinian militants and the arrest of about 400 wanted men in the West Bank.
But it says it will resume the operation if there are more Palestinian attacks.