The suspects can be held for up to 30 days before being taken to a judge to decide whether to remand them in custody, said an announcement in the official gazette, where all laws and decrees appear when they come into force.
Activists including Amnesty International had warned Turkey against expanding the detention period, which in normal times stands at a maximum of four days.
The statement added 1,043 private schools and 1,229 associations and foundations will be shut down under the state of emergency.
Turkey blames the coup attempt on the organisation of US-based preacher Fethullah Gulen whose influence runs deep in the Turkish education and legal systems.
According to the authorities, 10,410 people have been detained so far, including mainly soldiers but also police, judges, prosecutors and civil servants.
Of these, 4,060 people have been charged and placed under arrest so far, according to the state-run Anadolu news agency.
Among the latest to be remanded in custody is the female governor of the Black Sea province of Sinop, Yasemin Ozata Cetinkaya, the only regional governor to be detained so far.
At least 295 members of Erdogan's presidential guard-over a tenth of its entire membership-have also been detained over suspected links to the coup.
Meanwhile, 28 suspects detained over alleged links to a purportedly pro-Gulen whistleblowing Twitter account called Fuat Avni have been sent to court to be remanded in custody, the Dogan news agency said.
The government said the July 15 coup bid claimed the lives of 24 plotters, and of 246 citizens and members of the security forces who stood up to them.
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