The detentions came after the capital's public prosecutor issued arrest warrants for 260 suspects accused of using the encrypted ByLock messaging application which authorities believe was used to coordinate the coup bid.
Another 18 suspects, including 10 doctors, were sought in a second probe.
Officers have so far detained 171 people in Ankara and another 10 suspects elsewhere, the office said without giving details, AFP reported.
Tens of thousands have been arrested over alleged ties to US-based preacher Fethullah Gulen who Ankara says ordered the failed coup. Gulen denies this.
Since the failed overthrow of President Recep Tayyip Erdogan, authorities have also sacked or suspended over 140,000 public sector workers over suspected links to Gulen.