Hamas gunmen opened fire on forces of the rival Fatah, injuring at least six people, in another setback to a new security plan aimed at halting the wave of violence.
A further six people suffered gunshot wounds in family feuding unrelated to the conflict between the two organizations, Palestinian security officials said.
In the first phase of the plan to impose law and order, an estimated 3,000 police fanned out in Gaza City, taking up positions at main intersections and government buildings. The militant Hamas group is angered that Palestinian President Mahmoud Abbas of Fatah has not coordinated the new deployment with them.
In one incident, a minibus filled with Hamas gunmen opened fire at a Fatah security force manning a new roadblock. Palestinian medical officials said at least four people were wounded in this exchange.
In another attack, gunmen opened fire at the national security building in central Gaza and in the northern Gaza Strip two men were wounded when Hamas gunmen opened fire at their car.
Friday's shootings came after factional fighting Thursday in which one person was wounded and four people were kidnapped and then released in fighting in the strip's Nusseirat refugee camp.
After many months of clashes between the sides some Gazans are skeptical that the new police deployment would stem the unrest.
"They look good. But can they do anything? I doubt that very much," Badar Salim, 45, a Gaza City merchant said. "I hope this is something real, not just a show for the media."
The plan includes a joint operations room to be staffed by members of various security forces as well a joint security unit, said Ghazi Hamad, Prime Minister Ismail Haniyeh's spokesman. Hamad also said security commanders would hold meetings with leaders of Gaza's political parties and militant groups to maintain calm.
"Lawlessness and chaos have become very dangerous in Gaza, and all the participants are determined to end the chaos and restore security," he said.
Since Israeli withdrew from Gaza in 2005, the area has experienced a wave of infighting, armed robberies, deadly family feuds and kidnappings.
Attempts to halt the violence have failed, and the interior minister in the new Palestinian coalition government, Hani Kawasmeh, has threatened to resign because his plan for restoring security has not been carried out.
Hamas and Fatah formed a unity government in March with the aim of restoring calm. The alliance has brought a lull in factional fighting, but crime and violence remain rampant in Gaza.
Despite their power-sharing deal, Hamas and Fatah remain at odds over control over security forces. Hamas has its own force, and it was unclear how it would fit into the security plan.
Fatah has long demanded that the Hamas force be dismantled, but Hamas has refused.