"President Abbas has ordered the members of all the security forces to deploy as rapidly as possible in Palestinian towns to restore order and ensure security," an official said, asking not to be identified.
"Mr Abbas also told security force personnel to refuse any orders delivered by any authority but his own."
Members of a new security force recruited by the Hamas-led government fanned out across Gaza earlier on Wednesday in a deployment.
As two more Hamas followers were killed in overnight shootings linked to their dispute with Mr Abbas's Fatah faction, Hamas interior minister Said Siam said the new volunteer force would seek to restore order in a territory where gunmen have come to regard themselves as above the law.
"The current weakness of the security forces is clear to everyone. There is stealing, kidnapping and killing, so there is a real need for this force," he told a news conference.
The force would consist of 3,000 members drawn from all the Palestinian factions and would answer directly to his ministry, Mr Siam said.
Hundreds of members of the new force could be seen deployed in streets across the territory, clad in black T-shirts and combat trousers.
The forces, armed with Kalashnikov rifles and rounds of ammunition, took up position on street corners and landmark locations such as Palestine Square.
Minister Siam announced on April 21 he was creating a special force drawn from armed factions to supplement the work of police and security officers in clamping down on rampant chaos.
Mr Abbas, who has overall responsibility for security, initially dismissed the move as unconstitutional but subsequently indicated he would not take issue with the force if it acted as an auxiliary to the existing security apparatus.
"We agreed to allow a certain number of elements of different movements to join the security services, and the interior minister can therefore take in a reasonable number, as long as it is budgeted by the finance ministry," he told news agency AFP during a trip to Strasbourg, France.
Mr Siam insisted there was no disagreement over the force, which he said "has been formed in agreement with the office of the president."
The existing security services are dominated by members of Fatah, which has been involved in a growing number of clashes with followers of Hamas, which formed igovernment in March.
Shooting
Security sources said Wednesday that a Hamas follower had been killed in error overnight by gunmen from the faction's armed wing.
Bilal Abu Qasia, 30, of the Ezzedine al-Qassam Brigades, the armed wing of Hamas, died when two Brigades units in separate cars exchanged fire "by mistake" in Gaza's Jabaliya refugee camp.
He was shot just hours after a Hamas militant was killed by unknown gunmen in Gaza City, and a second shot and wounded west of Khan Yunis.
A bomb also exploded overnight at the home of a Fatah official, although there was no claim of responsibility.
Mr Abbas and Hamas leaders, including Prime Minister Ismail Haniya, have made a series of appeals in recent days for an end to the intra-Palestinian violence.
The new security force, however, seems likely to increase rather than ease friction.
"It is a dangerous escalation towards division led by the interior minister in announcing the work of this force which is part of the problem and not the solution," Fatah spokesman Tawfiq Abu Khussa told AFP.
"This force is only made up of men from the Qassam Brigades. This is a partisan force. Members of Fatah will not take part," he said.
A commander of one 25-strong unit of the new force acknowledged all his men were Hamas followers but insisted the force was not merely drawn from the Islamist faction.
"Members of the force come from all the factions. Right here it's all Hamas but really there are different factions involved," said Abu Mohammed in the central Gaza town of Deir el-Balah.