The order from Mahmoud Abbas came hours after the Hamas government defied the president by deploying its own security force onto Gaza streets.
"President Abbas has ordered all security forces, all branches to deploy men in the streets to restore order," a senior security official, who declined to be named, told Reuters.
He said it would be the largest such deployment in Gaza since police fanned out in force before last year's Israeli withdrawal from the coastal strip after 38 years of occupation.
Earlier on Wednesday, a new Hamas-dominated police force began patrols in the Gaza Strip in defiance of a ban by Abbas.
About 30 members of the new force, armed and wearing military fatigues, patrolled the market of Nussairat refugee camp, a Hamas stronghold in the Gaza Strip.
Some wore headbands emblazoned with the name "Qassam", after Hamas' armed wing – the Izz al-Din al-Qassam Brigades.
Prior to the deployment the interior minister of the Hamas-led government, Said Siyam, declared the security service operational after the deaths of two Hamas activists in drive-by shootings over the past two days.
These and other recent cases of infighting have threatened to plunge the Palestinian territories into bloody chaos.
Troops were deployed along
main roads as well
Witnesses said members of the force also deployed along main roads, including the north-south Gaza highway, and some were on mobile patrol.
The Hamas-led government and Abbas have been embroiled in a power struggle since Hamas defeated Abbas' long-ruling Fatah faction in the January parliamentary elections.
Abbas, who directly controls three security forces, appointed an ally as head of the remaining three security branches, which fall under the command of the Hamas-led interior ministry.
Siyam announced a plan last month to create the new force, which would be solely under his control.
Abbas vetoed the force, which is to number about 3,000 fighters and be headed by Jamal Abu Samhadana, an imoprtant figure in the ongoing rocket attacks on Israel and a suspect in the 2003 bombing of an American convoy in the Gaza Strip.
State of chaos
Ignoring Abbas, Siyam told a news conference on Wednesday that the unit would begin operating immediately.
He said the contingent would tackle a "state of chaos and anarchy and increasing assaults on our people".
Siyam (R) announced the plan
last month to create a new force
Just hours after the announcement, members of the new force ejected students from the local offices of the education ministry in the Gaza Strip town of Khan Yunus, where they were protesting against exam fees, witnesses said.
Tawfiq Abu Khussa, a Fatah spokesman, called on Siyam to "retract a hasty decision that may lead our people to catastrophe".
The prime minister, Ismail Haniya, later met leaders of his Hamas faction and Fatah to try to calm tensions.
Three gunmen were killed and a dozen people wounded in violence between Abbas' long-dominant Fatah and Hamas last week.
The clashes were fuelled by a power struggle between the president's loyalists and Haniya's supporters.
Siyam said attacks by "armed gangs" were part of "a plot to destabilise the Palestinian territories and match the pressure being applied on the government".
He said the security services he oversaw had been unwilling or unable to implement his orders.
Hamas' defeat of Fatah has caused Western aid cuts designed to pressure Hamas to recognise Israel and disarm.
The sanctions left the Hamas-led government unable to pay government salaries for more than two months.