Some 6000 members of the judiciary and military, including generals, have been detained.
Turkish forces loyal to President Recep Tayyip Erdogan largely crushed the attempted military coup on Saturday after crowds answered his call to take to the streets in support of the government and dozens of rebels abandoned their tanks.
Official figures put the number of civilians and police killed at 161, while 104 soldiers involved in the coup also died. The number of injured was 1440.
President Recep Tayyip Erdogan vowed to purge state bodies of the "virus" that caused the revolt.
US Secretary of State John Kerry has stressed the importance of democratic rule.
Speaking in Brussels where he has been meeting European foreign ministers, Mr Kerry said the United States stood squarely on the side of the elected leadership in Turkey.
"We will certainly support bringing perpetrators of the coup to justice - but we also caution against a reach that goes well beyond that."
The Turkish government claims cleric Fethullah Gulen was behind the plot.
Mr Gulen lives in the US and strongly denies any involvement.
State media reported on Monday that more than 100 generals and admirals had been detained in raids across the country.
Eight Turkish military officers who fled to Greece by helicopter appeared in court in the Greek border city of Alexandropouli charged with entering the country illegally. Proceedings were adjourned until Thursday.
Turkey has requested their extradition; they have applied for asylum in Greece.
President Erdogan told a crowd on Sunday that Turkey would consider reinstating the death penalty.
Capital punishment was abolished in 2004 as part of Turkey's bid to join the European Union. Nobody has been executed in the country since 1984.
European Union's foreign policy chief Federica Mogherini stressed the importance of the rule of law prevailing, and said ministers shared concerns about "what is happening in Turkey in these hours" - a reference to the rounding up of suspects.
"We need to respect, have Turkey respect, democracy, human rights and fundamental freedoms," she said.
Turkey has a long-standing application for EU membership and Johannes Hahn is the commissioner in Brussels dealing with it.
He said it appeared the Turkish government had pre-prepared lists of people to arrest before the coup attempt.
But the Turkish government says that the reason it has moved so fast is because it had been gathering evidence of what it calls a "secretive organisation" working within state structures, even before the failed coup.