Those who left Sidon comprised Syrian mothers with children and Palestinians living in Syria, the official said.
Lebanese troops defeated Fatah al-Islam fighters at Nahr al-Bared in September, after fifteen weeks of fighting.
Dozens of Fatah al-Islam fighters were killed in the crisis, the heaviest internal armed conflict since the end of Lebanon's 1975-1990 civil war.
Many other Fatah al-Islam fighters were captured while some escaped, such as al-Abssi.
Early on Wednesday, the families boarded two Lebanese general security buses in front of the al-Arqam Mosque.
In late August, 25 wives of Fatah al-Islam fighters were evacuated with their children from the besieged Nahr al-Bared camp,
The evacuation paved the way for the Lebanese army to launch a final assault and take full control of the camp.
The general security official said the six families that remained in Sidon included four Jordanians that their country refused to receive and two Syrians who did not have the proper documents.
Sheik Ali al-Youssef of the Palestinian Scholars' Association said contacts were continuing with Jordanian and Syrian officials.
Also on Wednesday, a Lebanese court sentenced Hani Badr al-Sankari, al-Abssi's son-in-law, to three years imprisonment for falsifying Lebanese identity cards and Palestinian refugee documents, judicial officials said.