A statement by the Islamic Resistance in Iraq, an umbrella group representing several Iraqi armed factions with close ties to Tehran, said five of its members had been killed, and vowed retaliation.
So far, at least 56 US personnel have suffered everything from minor wounds to traumatic brain injuries, though all have returned to duty, the Pentagon has said.
A Houthi military spokesperson said they shot down the drone in airspace over Yemeni territorial waters.
US officials have said 10 Americans who remain unaccounted for may be among the more than 200 people taken as hostages into Gaza.
For weeks, the US Army has deferred questions about whether King would face disciplinary action.
Army Sgt. Bernard J. Sweeney will be buried in New York next week on Tuesday.
This is the latest helicopter raid by US forces in Syria and appears to be part of an increase of these types of operations.
"Look at his words - STUPID & VERY DANGEROUS!" Trump wrote on his Truth Social platform.
According to US reports, a "mishap" caused an unnamed Marine Corps pilot to abandon his aircraft over the southeastern state.
People in the region are independent and have complex alliances and allegiances.