Abbas also named an interim national security chief to replace Haj Ismail, who resigned on Saturday after being asked to quit for failing to halt lawlessness, an official said on Sunday.
Both steps were prompted by Thursday's rampage by Palestinian gunmen, who fired at Abbas' compound in the West Bank town of Ram Allah in protest at a request by the Palestinian Authority that they lay down their arms.
Abbas is struggling to reform corruption-tainted security forces and impose order after declaring a truce with Israeli Prime Minister Ariel Sharon in February.
Israel's wanted list
The security source told Reuters that Abbas had issued a decree giving committees of officials in Gaza and the West Bank two weeks "to resolve the issue of the fugitives" - about 530 militants on Israel's wanted list for attacking Israelis.
Under the decree, the wanted men would voluntarily disarm and then be recruited as officials in the Palestinian government, the source said.
Once disarmed, Israel would no longer pursue these fugitives, added the source, reflecting a deal Abbas had reached with Sharon as part of the ceasefire they declared on 8 February.
Abbas, elected two months ago to succeed Yasir Arafat, has preferred to end four and a half years of conflict through dialogue rather than force, a tactic that helped him win a deal last month with militants to cement the truce with Israel.
But some militants have continued to resist Abbas' efforts to streamline security in the Palestinian territories.
Security head named
Thursday's rampage outside the Ram Allah office followed the expulsion from Abbas' compound of more than 20 gunmen who had once sought refuge there.
The Palestinian leader moved to restore order on Sunday by naming Nidal al-Assuri, a veteran security agent, as an interim head of national security in the West Bank, a day after the former commander had quit over the Ram Allah incident.
Separately, the West Bank intelligence chief, Tawfiq al-Tirawi, withdrew his resignation over the shootings, at Abbas' behest.
"You know there is a need to maintain the rule of law," Palestinian officials quoted Abbas as telling al-Tirawi on Sunday.
"This phase requires tremendous efforts, and I have full trust and faith in you."