ISTANBUL — The United States said on Sunday that it was suspending nonimmigrant visa services at its diplomatic facilities in Turkey after the arrest of a consulate employee, prompting Turkey to halt visa services in America.

The United States Embassy in Ankara, the Turkish capital, issued a statement from the United States Mission to Turkey saying that recent events had forced it to “reassess the commitment of the government of Turkey to the security of U.S. Mission facilities and personnel.”

The Turkish Embassy in Washington responded with a similar statement late Sunday, saying it would “reassess the commitment of the government of the United States to the security of Turkish mission facilities and personnel.” It said the measures would apply to e-Visas, visas issued at borders and visas in passports.

Last week, the Turkish authorities arrested a United States Consulate employee of Turkish nationality over alleged links to the network of the United States-based cleric Fethullah Gulen, whom the Turkish government blames for last summer’s failed coup. Mr. Gulen denies involvement. The employee, Metin Topuz, is accused of espionage and “attempting to overthrow the Turkish government and constitution.”