The battle for eastern Aleppo, where the United Nations says some 275,000 people are besieged, has raised tensions between the United States and Russia to their highest levels in years, but the Cold War rivals do not wield clear control over their nominal proxies. The competing interests on both sides and lack of clear leadership on either one is part of why the fighting has proved so hard to stop: Mr. Assad is desperate to retain power, Moscow is seeking to increase its clout at the global geopolitical table, and Iran is exercising its regional muscle.

While Washington and Moscow say preservation of Syrian state institutions is a priority, a look at the fight for Aleppo, Syria’s largest city, shows that those structures are already atrophying.

At least one elite Syrian Army unit has been filmed seizing positions in Aleppo, but the bulk of the pro-government force is made up militiamen trained and financed by Iran, the Shiite theocracy that is the Syrian government’s closest ally, according to experts, diplomats, regional officials and fighters battling for and against the government.

“Aleppo is Shiite, and she wants her people,” goes a song overlaid onto a video posted online of an Iraqi cleric visiting Iraqi Shiite militia fighters on the front lines south of Aleppo. The message ignores the fact that the mainstream Shiite sect that accounts for the bulk of the Iraqi militias makes up less than 1 percent of Syria’s population.