"The (Al-Aqsa) Martyrs' Brigades in the Gaza Strip decided to deploy a protection unit of 1,250 fighters," said the faction, which is loosely affiliated to the once dominant Fatah party of Palestinian Authority president Mahmud Abbas.
The statement said that the objective would be to "protect the Palestinian resistance from aggressions of Zionist special units. They will be deployed on the borders of the Gaza Strip."
Four Palestinians, including three members of the Islamic Jihad faction, were killed last Tuesday during the first Israeli special force operation in the Gaza Strip since Israeli troops left the territory last year.
Al-Aqsa delivered the statement just 24 hours after about 2,500 members of a new armed force loyal to Mr Abbas deployed in the volatile northern West Bank city of Jenin and two weeks after Hamas fielded a similar force in the Gaza Strip.
Al-Aqsa also threatened to deploy members of the "unit" in the streets of Gaza if "assassinations by unknown (gunmen) continue," a reference to recent deadly feuding that has killed both Fatah and Hamas supporters.
"We will deploy this unit in the main streets of the Gaza Strip to protect Palestinian citizens," the group said.
There was no immediate reaction from Hamas or the government and no date announced for the deployment of the Al-Aqsa patrols.
However if the patrols are put in place the move is likely only to send Palestinian tensions soaring.
Members of a "Special Protective Force" have taken to the streets of Jenin clad in black T-shirts emblazoned with pictures of the late Palestinian leader Yasser Arafat.
Any new deployments are likely only to escalate tensions between Hamas and Fatah, which flared into clashes in which 11 people were killed in recent weeks, despite an ongoing national dialogue aimed at defusing them.
Al-Aqsa's declaration came with Hamas under mounting pressure to accept a document seeking to end the deadly feuding and financial torment as Mr Abbas prepared to deliver on a threat to put it to a referendum.
Hamas and Fatah have been locked in a power struggle since the Islamists ousted the long-ruling Fatah party in parliamentary elections in January.
Much of their rivalry since Hamas's election victory has centered around control of the Fatah-dominated security services which remain the remit of Mr Abbas as president of the Palestinian Authority.