The exile coalition hopes the battles will persuade the West that the insurgents, not Mr. Assad, can best stop Al Qaeda from establishing a base in the country. That security threat has made foreign powers, not to mention many Syrians, more open to accommodation with the government.

Advocates of increased Western aid to the rebels argue that the fighting shows that the Islamic Front, a collection of Islamist Syrian groups now fighting ISIS, is not a Qaeda-like threat. But many of its leaders, and even some in other groups that nominally answer to the exile coalition, say they have no quarrel with the main Qaeda affiliate, the Nusra Front.

Nusra, indeed, could be the main beneficiary of the scuffling. Taking a more pragmatic approach has helped Nusra recruit many Syrian fighters and could now enable it to cement alliances, rid itself of a rival for Qaeda-inspired donations, absorb foreign fighters fleeing ISIS and embed itself more deeply in society. In trying to mediate the dispute, it has also set itself up as peacemaker and power broker.

But Nusra has come in for its own share of criticism for clashes with rebel groups, killing civilians and branding minority Shiites and Alawites as the enemy. For the West and for secular Syrians, said Michael Hanna, an analyst at the Century Foundation, “Nusra, because they are more pragmatic, are a much more intractable problem.”

The picture is further complicated by the fluidity of alliances. In the highly localized conflict, ISIS and its rivals remain united even now against Kurdish militias in the northeast. Fighters often switch factions, not always sharing the views of nominal leaders, and sometimes Qaeda trappings signify branding more than chain of command.

Some homegrown rebels say they are fighting ISIS to reclaim the insurgency from extremists and regain trust from supporters who want a pluralistic Syria. Others say they want to salvage an Islamist movement stained by the extreme brutality of ISIS and its zeal for attacking fellow Sunnis.

“They call themselves Qaeda because they know the young fighters love our great sheikh Osama bin Laden,” said Abu Ibrahim al-Masri, an Egyptian fighter near the central city of Hama. He spoke in a video announcing that he was defecting from ISIS to Nusra because he had been ordered to kill civilians and members of the rebel Free Syrian Army instead of army soldiers and, as he put it, Alawites.