The confrontations began after midnight with a spate of kidnappings and peaked at daybreak when Hamas fired a shoulder-held missile into a Jeep with government licence plates, killing two Fatah gunmen who were also members of the security forces.
The fighting was the latest sign the two sides could be sliding towards large-scale clashes.
Tensions have been rising since Hamas ended Fatah's four-decade control of Palestinian politics with a victory in January parliamentary elections.
Hamas and the Palestinian president, Mahmoud Abbas of Fatah, have been wrangling over power, particularly over control of the security forces, and the friction has been compounded by a growing financial crisis, a result of Western economic sanctions against the Hamas-led government.
Abbas and the prime minister, Ismail Haniya of Hamas, failed to resolve their differences in weekend meetings.
The violence on Monday began before dawn in the farming community of Abassan in southeastern Gaza. Hamas tried to kidnap a Fatah member, apparently to settle an old score dating back to the January election, said Tawfiq Abu Khoussa, a Fatah spokesman.
The two sides exchanged fire, and a Hamas member was seriously wounded, Abu Khoussa said.
The shooting prompted a series of kidnappings in which Hamas seized three Fatah members, and Fatah briefly captured four Hamas militants. The captives were released after negotiations.
Tension between Fatah and
Hamas has been rising
However, the Hamas member wounded in the initial firefight later died of his wounds, and his death triggered a new round of fighting with assault rifles and submachine guns.
Gunmen hiding in fields exchanged fire across Abassan's main road, sending civilians ducking for cover.
At one point, Hamas fighters ambushed Fatah members driving along the main road in two Jeeps with red Palestinian Authority licence plates. One vehicles was hit by a shoulder-held missile and the second was riddled with bullets.
Ten men were wounded, including one who was in a serious condition.
Ghazi Hamad, a spokesman for the Hamas-led government, urged calm and said efforts were under way to stop the fighting.
"The interior ministry is following up the issue," he told Aljazeera. "They have ordered policemen and security forces to stop the events and control the situation in the streets. There are also talks going on between Fatah and Hamas."
Abu Khoussa said he held Hamas responsible, accusing the group of inciting Fatah.
In other developments on Monday, Israel said it is in the process of mapping unauthorised construction in the West Bank, according to a court document. The Israeli government has stalled for three years on its promise to the US to take down wildcat settlement outposts.
Critics attacked the latest initiative as another Israeli delay tactic, noting that a year ago, a government-commissioned report detailed 105 unauthorised outposts. Almost all of them are intact, and other unauthorised structures have been erected in the West Bank since.
A deposition filed by the Israeli military with Israel's Supreme Court said the state would draw up a plan to dismantle the unauthorised construction it is mapping. Although it said the mapping would take four months, it gave no timetable for taking down the buildings.