At least one of the wounded was said to be in very serious condition.
They said the gunmen opened fire as about 200 Hamas activists and armed men were preparing for a rally in the city of Nablus. There was no immediate comment from Fatah.
Violence between the rival factions has erupted since Abbas called for early elections a week ago. The two sides agreed on a cease-fire in the Gaza Strip earlier this week, following days of fighting that killed 10 people there.
Despite the two-day-old truce, a series of heavy gunbattles between Hamas and Fatah militants broke out in Gaza City early Friday.
The gunfights erupted near the Hamas-controlled Foreign Ministry and the Gaza residence of Palestinian Authority Chairman Mahmoud Abbas, of Fatah. The fighting died down after about 20 minutes, as Muslim clerics and other mediators worked to restore the cease-fire. Abbas was not in Gaza at the time.
In Gaza City on Friday, Prime Minister Ismail Haniyeh of Hamas urged gunmen to spare Palestinian blood, and said government officials were working to bring the violence under control.
The violence came after a Hamas militant, Mahmoud Al-Lali, was kidnapped late Thursday night by armed men, who fired assault rifles in the streets and seriously wounded a bystander.
The factional fighting also played out on the bureaucratic level Friday. In a letter to Haniyeh, Abbas chief of staff Rafiq Husseini deemed five senior Hamas appointments to the Palestinian Authority to have been illegal.
Adnan Amr, a legal adviser to Abbas, said the president rejected 40
appointments in all.
In a related development, a top Abbas aide, Azzam al-Ahmed, reiterated the Palestinian president's offer on Thursday to resume coalition talks with Hamas, but said the offer would only be good for a week or two.
On Friday, Haniyeh pronounced Hamas ready to resume negotiations, but
indicated the group would continue to reject the international demands. "We are ready to begin discussions on a unity government on the basis of Palestinian conditions," he said.
However, after the funeral of the two men who had been killed, Fatah members in attendance went on a rampage near the cemetery where the bodies were buried, torching several cars believed to belong to Hamas.
Four cars were riddled with gunfire and badly charred, and smoke covered the windows of a nearby building belonging to the local electric company. The destroyed vehicles turned out to be cars belonging to the company.
Two TV cameramen filming the incident were roughed up by protesters, who also confiscated their videotapes and smashed them.
Gaza residents reported gunfire between rival fighters minutes after the truce, which was brokered by Egyptian mediators, went into effect Tuesday night.
A previous truce between the ruling Hamas faction and once-dominant Fatah, signed Sunday, broke down within 24 hours.
Gunbattles between Hamas loyalists and Fatah forces Tuesday also left at least 18 people wounded, medical officials said, including five children caught in the cross-fire.