The Arab plan required Syria to halt the bloodshed, withdraw troops from cities, free detainees, provide access for the monitors and the media and open talks with opposition forces.
Rebel commander Asaad opposed any extension of the mandate.
"The Arab League and their monitors failed in their mission and though we respect and appreciate our Arab brothers for their efforts, we think they are incapable of improving conditions in Syria or resisting this regime," he told Reuters.
"For that reason we call on them to turn the issue over to the U.N. Security Council and we ask that the international community intervene because they are more capable of protecting Syrians at this stage than our Arab brothers," Asaad said.
Syria would agree to an increase in the number of monitors, he said, but would not allow them to be given formal fact-finding duties or be allowed into "military zones" that are not included in the existing Arab peace plan.
Any change in the scope of the mission, whether to militarise it or let it investigate human rights abuses and potentially assign blame, would require a new agreement with Syria, the source said.
Qatar has proposed sending in Arab troops, a bold idea for the often sluggish League and one likely to be resisted by Arab rulers close to Assad and those worried about unrest at home.
Syria's foreign ministry said on Tuesday it was "astonished" at Qatar's suggestion, which it "absolutely rejected".