Relatives and members of factions, some armed and wearing camouflaged uniforms, joined a convoy taking his body to the city's Al-Othman Mosque and then on to the cemetery at the Palestinian refugee camp of Yarmouk.
"Before he died he said that during this long struggle he never sold his principles or gave up and we shouldn't either," Khaled Jibril, his son and the group's director of military and security, told Reuters.
Ahmed Jibril, who died on Wednesday aged 83, founded his PFLP-GC in 1968 after splitting from the PFLP of Palestinian nationalist leader George Habash.
In its early years, the PFLP-GC, designated as a terrorist group by the United States, carried out dozens of attacks in the Middle East and Europe, including airplane bombings, kidnappings and letter bombs.
Jibril was long at odds with the late Palestinian leader Yasser Arafat and his successor Mahmoud Abbas over peace accords with Israel.
Jibril had fought alongside Syrian government troops to retake Yarmouk during Syria's decade-long conflict and was criticized by some Palestinians for aligning his group behind President Bashar al-Assad's forces throughout the war.
His funeral was attended by the Iranian ambassador in Damascus, leaders of Palestinian factions in Syria and top officials from Syria's ruling party.
Jibril's youngest son, Mohamed Bader, led the prayers over the coffin which was draped with the Palestinian flag.