Turkey has kept the crossing closed since Sept. 19 because of security concerns, a Turkish Foreign Ministry official said.

Seeking to end the crisis, a group of six powerful rebel brigades released a statement late Wednesday calling for an immediate cease-fire.

In a jab at the strict ideology of the ISIS jihadists, the statement told them not “to shed the blood of Muslims and be hasty in calling them heretics and apostates.” It also called on both sides to submit themselves to the Shariah Commission, a rebel-run court in the northern city of Aleppo, within 48 hours to resolve the problem.

It was unclear if the ISIS fighters would heed the call.

The rise of ISIS in rebel-held areas in northern and eastern Syria has posed a problem for the broader rebel movement. While many insurgents are deeply Islamist themselves, their focus remains on toppling Mr. Assad, and they accuse ISIS of prioritizing its own jihadist agenda over the fight against the president. But the rebels hesitate to confront ISIS, saying their resources are already stretched by fighting the government.