State Department spokesman Ned Price confirmed on Monday evening that Mr Flake went to the Turkish Foreign Ministry for discussions, media have reported.
Gen Milley made an unannounced visit on Saturday to review a nearly eight-year-old US occupation presence in the east of Syria to SDF-controlled areas.
Turkey considers SDF as being an offshoot of the PKK, which is also designated a terrorist organization by the EU and the US.
Syria’s foreign ministry on Sunday condemned the unannounced visit of the top US military officer to a US base in northeast Syria as “illegal” and a “flagrant violation” of the country’s sovereignty.
The legitimate Syrian government in Damascus led by President Bashar Assad considers the presence of the American and Turkish forces on Syrian soil as illegal and occupation and has called for their immediate withdrawal to exercise its sovereignty over all the Syrian territories.
MNA/PR