Updated

Iraqi militia fighters are pouring into Syria to reinforce the Assad regime’s siege of rebels in Aleppo, further complicating the tangled web of alliances the U.S. relies on to fight Islamic State, which can turn an ally on one side of the border into an enemy on the other.

The Shiite militias, who have fought alongside U.S.-backed Iraqi government forces against Islamic State in Iraq, are now fighting Syrian Sunni rebels, some of them armed and trained by the U.S.

More than 1,000 Iraqi Shiite militants have traveled from Iraq since early September, joining the ranks of as many as 4,000 others already on the ground near Aleppo, the militia leaders and Syrian rebels said. They make up about half of the regime’s estimated ground force of 10,000.

The siege they are helping to enforce has tilted the battle there in favor of President Bashar al-Assad, whose ruling Alawite sect has drawn on fellow Shiite powers to shore up government forces depleted by deaths, defections and attrition over five years of war: Iran’s Revolutionary Guards Corps, Lebanon’s Hezbollah militia and Afghan Shiite fighters.

The regime, along with its ally Russia, has been heavily bombarding rebel areas of the divided city over the past few weeks. The offensive has killed hundreds, including scores of children, and caused the collapse this week of joint U.S.-Russian efforts to forge a lasting cease-fire and restart talks on a political solution

In an update on the Aleppo situation published on Tuesday, the United Nations Office for Coordination of Humanitarian Affairs said living conditions for the roughly quarter of a million people in besieged neighborhoods of eastern Aleppo have deteriorated, and “an assessment conducted in eastern Aleppo city concluded that 50% of the inhabitants expressed willingness to leave if they can.”

Hashem al-Mosawwi, a commander of the Iraqi Shiite militia Al Nujaba, or “The Noble Ones,” said his group deployed 1,000 fighters to Aleppo in September—the latest influx of Shiite fighters in recent weeks—and that he sees their involvement as part of a larger regional struggle against terrorism. Other militia leaders said they also sent fighters recently, without giving numbers.

Mr. Mosawwi claimed the rebels in Aleppo are part of an extremist Sunni axis sponsored by Saudi Arabia and the U.S.

“Those…terrorist groups cause all problems in the region and the world and they should be stopped,” he said, naming several Sunni opposition groups in Syria he deems synonymous with the Sunni extremists of Islamic State. The Syrian opposition is dominated by the country’s Sunni majority.

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