New threats raise the possibility of a clash between NATO allies.
There were no signs of further clashes between pro-Turkish forces and Kurdish militia groups that had controlled the city.
Despite strains in the U.S. relationship with Turkey, the Air Force says operations at the air base remain unaffected.
"Ankara is looking to define a new role for itself as a champion of Sunni interests and as a leader of the Islamic world."
Ankara's campaign against the Kurdish YPG is forcing the U.S. to pause its mop-up operations against ISIS.
Turkey wants no confrontation with U.S. troops, but said they risk being caught up in clashes if they wear YPG uniforms.
Syria's Kurdish militia is growing frustrated with its patron, the United States.
Turkey renewed threats over the weekend to attack a town in northern Syria where U.S. troops maintain an outpost.
Over the weekend Turkish forces launched an incursion into Afrin, a border canton defended by the YPG militia.
Intense fighting flared Monday as Turkish troops and their allies advanced on a Kurdish enclave in northwestern Syria.