Troops began deploying across main West Bank cities late on Saturday, hours after Abbas ordered similar measures in Ram Allah after an incident on Wednesday in which gunmen opened fire inside his headquarters, the Muqataa compound.
The order was given at a top-level meeting between Abbas and his security chiefs late on Saturday.
At the meeting, Abbas also gave the order for all branches of the sprawling Palestinian security services to be relocated outside his compound.
The order, effective immediately, will see the offices of the national security, military intelligence and police, among others, rehoused on a large tract of land about a kilometre from the Muqataa.
Only the presidential guard, Force 17, will remain in the compound.
The move came hours after Abbas sacked West Bank national security chief General Haj Ismail Jabir, and Ram Allah security chief Yunis al-Has over the shooting incident. Intelligence chief Tawfik al-Tirawi handed in his resignation, but it was not accepted by the Palestinian leader.
The shake-up was provoked after a group of renegade gunmen, allied with the dominant Fatah faction, opened fire inside Abbas' compound.
There were no casualties, but the outburst embarrassed Abbas, also known as Abu Mazin, who has repeatedly pledged to restore security.
Jabir is reported as giving four reasons for his resignation: the deteriorating security situation and the hesitation of the political leadership to unite security apparatuses; the failure to tackle the issue of wanted activists; the implementation of the law on the powerless only; and the personal incitement campaign of Israel's Defence Minister Shaul Mofaz against him.
Aljazeera's bureau chief in Palestine Walid al-Umari said Abbas' move came as a result of the failure of security apparatuses in halting lawlessness.
Palestinian national security adviser Jibril al-Rajub said on Saturday: "Abu Mazin has no choice but to impose law and order to achieve security for Palestinian citizens as he promised in his campaign.
"This can only be achieved by reviewing the security hierarchy, as well as conducting the necessary transfers among the leaders of the security organisations and activating the retirement law."
Such moves were crucial to formulate a professional, productive security establishment able to meet its obligations on a regional, national and international level, he said.
Hamas has decided to contest
A Palestinian official said several names were being studied to fill the vacancies left by the dismissals and resignations, with al-Rajub tipped as the leading contender for Jabir's position.
Earlier on Saturday, Abbas repeated promises to assure the security of the population and to end disorder and chaos.
Fatah would not allow anarchy to take over on the ground, as that would benefit Hamas, an official added, referring to the resistance movement that is to run in legislative elections in July.
The Palestinian Authority is also pushing ahead with plans to trim the burgeoning security forces and to prosecute those involved in corruption.
Abbas gave the go-ahead for a retirement scheme that will see high-ranking officials over the age of 60 compelled to step down.
The Palestinian parliament has approved the scheme which will trim several hundred officials from senior ranks in the security services.
The retirement scheme was not
implemented under Arafat
The Palestinian leadership had been reluctant to implement the scheme during former President Yasir Arafat's tenure.
Another Palestinian official said the attorney general had started investigating four officials on suspicion of misusing public funds.
Three of them are high-ranking officials from the Finance Ministry, while the fourth is a former special secretary to the late Palestinian leader Arafat.
West Bank protest
Also on Saturday, Israeli occupation forces fired tear gas and rubber bullets to break up a demonstration against Israel's separation barrier north of Tulkarim in the West Bank, Aljazeera reported.
Dozens of Palestinians, including ministers and other officials, and foreign activists participated in the protest, calling for a removal of the barrier and an end to Israeli settlements.