Abbas, who was in the building but was not hurt in the gunfire late on Wednesday, ordered a crackdown.
Security officials said the renegades had "crossed a red line" by attacking the seat of government.
Later, the officials adopted a conciliatory line, and one admitted they feared coming under armed attack themselves.
Earlier, in a meeting with security officials after the shooting spree, Abbas ordered the group arrested, more troops deployed throughout the city and compensation paid to the businesses that were damaged, security officials said on Thursday.
The men say security staff forced
them to quit the Ram Allah HQ
The incident began with an armed group of 15 attacking the compound on Wednesday before rampaging through the city, damaging several restaurants and forcing shops to close, witnesses and officials said.
There were no injuries reported.
The armed men, who said they were members of the al-Aqsa Martyrs' Brigades, an armed group linked to the ruling Fatah movement, said they went on their rampage after Palestinian security officials forced six of them out of the Ram Allah headquarters, where they had sought refuge after Israeli forces began hunting down fugitives shortly after violence erupted in September 2000.
A Palestinian security official, speaking on condition of anonymity, said the security forces told the six armed men to either hand over their weapons or leave the compound after "they were involved in kidnappings, blackmailing, harming people, shooting them".
Another security official, also speaking on condition of anonymity, warned that the security forces were considering taking harsh steps against the group.
"They have crossed the red line. They attacked the presidential headquarters. They are defying the Palestinian Authority and now we have to take harsh steps against them, otherwise they will control the city and spread chaos," the official said.
Also on Thursday, police in the West Bank town of Tulkarim demanded the surrender of seven armed Palestinians who burned down a Palestinian checkpoint overnight.
"They are defying the Palestinian Authority and now we have to take harsh steps against them, otherwise they will control the city and spread chaos"
Palestinian security official
"If they don't, there will be war," one official said on condition of anonymity.
The ultimatum was issued following the incident late on Wednesday when a mob of angry Palestinians burned down a Palestinian roadblock outside Tulkarim after officers shot and wounded a man, security officials said.
The officers stopped three men, reportedly suspected car thieves, and after an argument, a police officer shot and lightly wounded one of the men.
A large group of men, some of them armed, then stormed the roadblock. The police fled, and the protesters burned several tents used to house the officers and the Palestinian flag that flew above.