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– Thousands of Islamic State of Iraq and Syria foreign fighters and family members have escaped the U.S.-led military campaign in eastern Syria, according to new classified U.S. and other Western military and intelligence assessments, a flow that threatens to tarnish U.S. declarations that the militant group has been largely defeated.

As many of the fighters flee unfettered to the south and west through Syrian army lines, some have gone into hiding near Damascus, the Syrian capital, and in the country’s northwest, awaiting orders sent by insurgent leaders on encrypted communications channels.

Other militants, some with training in chemical weapons, are defecting to Al-Qaida’s branch in Syria. Others are paying smugglers tens of thousands of dollars to spirit them across the border to Turkey.

The sobering assessments come despite a concerted effort to encircle and “annihilate” — as Defense Secretary Jim Mattis put it — ISIS fighters in Raqqa, the group’s self-proclaimed capital, which fell in the fall, and pursue other insurgents who fled south into the Euphrates River Valley toward the border with Iraq.

“ISIS fighters are fleeing Syria and Iraq,” Homeland Security Secretary Kirstjen Nielsen said in remarks in Washington last week, using an acronym for Islamic State. “Jihadis are going underground, dispersing to other safe havens, including on the internet, and returning to their home countries.”

While President Donald Trump highlighted the liberation of almost all of the ISIS territory in Iraq and Syria in his State of the Union address last week, U.S. military and intelligence officials say the group is still able to inspire and enable followers to carry out attacks.

Asked late last month by the New York Times about indications that as many as 1,000 fighters and family members had fled the Euphrates River area in recent days, the command of Col. Ryan Dillon, chief spokesman for the U.S.-led military campaign in Iraq and Syria, replied in a statement: “We know that the Syrian regime has given ISIS the leeway to travel through their area of operations, but we cannot confirm any alleged incidents or operations that are taking place outside our area of operations.”