Palestinian sources said the three had been shot by Israeli forces near the centre of town but the army said the casualties were a result of a crash that followed attempts by the driver to evade arrest.
The dead man was named as 24-year-old Ahmed Musla, a member of the Al-Aqsa Martyrs Brigades which is a radical offshoot of the former ruling Fatah faction.
An Israeli army spokeswoman said that the deaths occurred after the occupants of the vehicle tried to bypass a checkpoint which had been erected in order to capture the trio.
"When they drove off the road, the forces called on them to stop and then fired shots in their direction, which were not aimed to kill, and the car crashed into a wall.
"As a result of the crash, a fire broke out and one of the wanted man was killed and the two others were wounded," he said.
Gaza shootout
Tensions between the Hamas-led government and President Mahmoud Abbas's Fatah faction flared into a shootout at the Palestinian Health Ministry, despite pledges to calm an eruption of internal fighting.
At least four people were wounded after gunmen from Fatah's al-Aqsa Martyrs Brigades stormed into the ministry, where they were confronted by Hamas guards.
An al-Aqsa spokesman denied the men were from his faction, saying they were from a Gaza clan affiliated with Fatah.
The guards from Hamas's Izz el-Deen al-Qassam brigades chased off most of the Fatah intruders and captured four of the gunmen, tying them up and putting them into a police car as people in the street cheered.
About 20 people were hurt in armed confrontations in Gaza between students and militants from Fatah and Hamas. It was the most serious fighting between Palestinians since Hamas won a parliamentary election in January.
The violence followed the condemnation by exiled Hamas leader Khaled Meshaal of Abbas's veto of a new Gaza security force formed by the Islamic group and headed by a top militant.
The appointment of Jamal Abu Samhadana, head of the Popular
Resistance Committees which has often attacked Israel, as leader of the new Gaza police force was widely seen as an attempt by Hamas to strengthen its grip on the powerful Interior Ministry.
Mr Abbas cancelled the decision, a veto Mr Meshaal said assisted a Western campaign to isolate the Palestinian government.
Arab League funding
Sworn to Israel's destruction, Hamas has rejected Mr Abbas's calls to pursue a negotiated peace with the Jewish state.
The new government is also battling a crippling financial crisis after Israel cut off monthly tax transfers and Western governments halted direct aid. Salaries for 165,000 Palestinian Authority employees are already three weeks late.
But the Arab League said it intends to transfer $US50 million ($A67.94 million) this week to the Authority, enough to pay about 40 per cent of the overdue salaries.
In his latest audiotape Al-Qaeda leader Osama bin Laden said Western efforts to isolate Hamas, was an example of the West's "crusader war" against Islam.