The dispute was triggered by the arrest of local U.S staff in Turkey, prompting the United States on Sunday to suspend non-immigrant visa services there. Hours later, Ankara issued a similar suspension on visas for U.S. citizens.
U.S. Secretary of State Rex Tillerson spoke with Turkish Foreign Minister Mevlut Cavusoglu on Wednesday and expressed his "profound concern" about the arrests, the U.S. State Department said in a statement.
"Talks between the foreign minister and (U.S. Secretary of State) Tillerson were very constructive. Representatives from both sides decided to meet and work together," Bozdag said in an interview with broadcaster Haberturk.
He also said a U.S. consulate employee arrested in Turkey had not demanded lawyer access and the U.S. mission could apply to send a lawyer to see him.