"This initiative is the last remaining chance for besieged members of Daesh (IS) to leave the town," said the Manbij Military Council, part of the Syrian Democratic Forces (SDF) alliance.
The warning came two days after strikes launched by the US-led coalition fighting IS reportedly killed at least 56 civilians fleeing a town near Manbij.
Coalition warplanes have carried out intense raids in support of the SDF fighters as they seek to oust IS from Manbij and surrounding areas.
The statement also called for civilians to try to leave the town or distance themselves from areas where clashes are taking place.
It follows an intense backlash over the reported deaths of at least 56 civilians, including children, in US-led strikes on an IS-held village near Manbij earlier this week.
The deaths provoked local protests, as well as opposition calls for a halt to such strikes and demands for a thorough investigation.
The US-led coalition has said it is investigating reports of civilian deaths in the strikes.
"But we took this decision now after IS used residents as human shields, after the media pressure on us, and to protect whatever civilians are left in the town," the commander said on condition of anonymity.
Clashes and air strikes continued today in Manbij, where SDF forces advanced overnight, said the Syrian Observatory for Human Rights.
Observatory head Rami Abdel Rahman said SDF fighters seized a southern district of the town, "bringing them the closest they have been to the centre of Manbij.
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