Six Fatah members were killed, more than 70 people were injured and at least 12 members of both rival factions were kidnapped in the ensuing clashes.
Abbas' Fatah faction said the four-truck convoy, which crossed into Gaza from Israel, was carrying medical equipment and tents, and accused Hamas of plunging a 3-day-old ceasefire into grave danger.
Two presidential guard officers and two civilians were killed in a battle between Hamas gunmen and presidential guards accompanying the convoy, the residents said.
"A real war is taking place, gunmen are using the heaviest arms they have," said one witness, declining to be identified.
President George W. Bush has committed USD 86 million to provide training and non-lethal equipment to forces loyal to Abbas, a moderate. Weapons are being supplied by key US allies Jordan and Egypt, with Israeli approval, Israeli officials say.
Hamas defeated the once-dominant Fatah in elections a year ago. But it has struggled to govern since taking office in March under the weight of US-backed sanctions imposed over its refusal to recognize Israel, renounce violence and accept existing interim peace deals with the Jewish state.
Diplomats say Abbas' military build-up was meant to counter strides by Hamas in smuggling more powerful weapons into Gaza for its fast-growing "Executive Force" and armed wing, known as the Izz el-Din al-Qassam Brigades.
'There are no weapons at all'
Sources in Hamas said the trucks, which set off from the Kerem Shalom crossing point with Israel, were carrying weapons for the 4,000-strong presidential guard, a force loyal to Abbas and Fatah.
"Hamas' heroes have commandeered arms shipments that came through Kerem Shalom as part of the fight against the Palestinian people," a presenter on a Hamas radio station said.
Fatah spokesman Tawfiq Abu Khoussa said the convoy was ferrying generators, tents and medical equipment.
"There are no weapons at all," said Abu Khoussa, describing the ambush as representing "a grave danger to the continuation of the (ceasefire) agreement."
Residents said one of the vehicles was taken over.
Asked about the convoy's cargo, a Palestinian security official declined to comment. A senior Israeli official said she knew trucks had entered Gaza but did not know their contents.
Another 10 people were wounded in northern Gaza when Hamas raided a military intelligence post. Hamas said its forces came under fire first.
In the occupied West Bank, Israeli forces killed three members of Fatah's armed wing, al-Aqsa Martyrs Brigades, in the towns of Nablus and Tulkarm, residents and the military said.
Israeli military sources said troops in Nablus killed two al-Aqsa gunmen in a clash. The militant killed in Tulkarm was shot while trying to evade capture, the sources said.
Israeli troops shot dead a fourth Palestinian near Israel's West Bank barrier, hospital sources said. They said the 17-year-old bled to death after being wounded in the leg.
Ali Waked contributed to the report