Extremist fighters of the Islamic State group control a swath of land straddling Syria and neighbouring Iraq, mostly running across the Euphrates river, where they have established their self-styled caliphate.
Most of the land was seized last month in a lightening push across Iraq.
In recent days, fighters from the group have been pushing into rebel-held territory around the northern Syrian city of Aleppo, close to the Turkish border.
"We call on urgent support for the FSA with weapons and ammunition, and to avoid a humanitarian disaster that threatens our people," said Brig Gen Abdul-Ilah al-Bashir, commander of the Free Syrian army.
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"Time is not on our side. Time is a slashing sword," he said.
His statement underscored the distress many of the country's many rebel fighters, whose battle to overthrow President Bashar Assad has been overshadowed by the advance of Islamic State fighters.
In northern Syria, where the extremists have been pushing back rebels, Syrian government forces also seized a key industrial area, allowing them to choke off rebel-held parts of Aleppo, already brutalised by indiscriminate bombing.
He said the Islamic State fighters will not halt at Syria's borders.
"If we do not receive support quickly, the disaster will not stop at the borders. We put the international community before its historic responsibility," he said.
Also today, Syrian activists said that a father, mother and their six children were killed in a government airstrike in the southern town of Dael.
The Britain-based Syrian Observatory for Human Rights said the eight civilians were killed in shelling early today. The activist collective, the Local Coordination Committees, also reported the incident.