The Turkish Prime Minister, Binali Yildirim, has vowed to purge supporters of an exiled cleric "by the roots" in the aftermath of the failed coup.
He said he had sent the US evidence of Fethullah Gulen's criminal activities - allegations the cleric denies - in support of an extradition bid.
Mr Yildirim insisted that his country was governed by the rule of law.
Thousands of soldiers, police and officials have been detained or sacked since Friday's coup attempt.
President Recep Tayyip Erdogan has again refused to rule out reinstating the death penalty for coup plotters if it is approved by parliament.
The EU has warned that such a move would see the end of accession talks to the bloc.
For now, at least, that seems not to worry President Erdogan, who is seizing the opportunity to tighten his grip, reports the BBC's Turkey correspondent, Mark Lowen.
Prime Minister Yildirim was speaking after meeting the leader of the main opposition CHP party.
He warned people not to act out of a spirit of revenge in the wake of Friday's failed military takeover, saying that would be "unacceptable" but whoever had acted against the law would be punished.
"Today we need unity," he said.
The interior ministry has dismissed almost 9,000 police officers as part of a purge of officials suspected of involvement in the coup attempt.
That followed the arrest of 6,000 military personnel and suspension of almost 3,000 judges over the weekend.
Many of those accused of involvement are closely linked to the ruling apparatus.
National security takes a blow: analysis by Doruk Ergun, Centre for Economics and Foreign Policy Studies, Istanbul
Turkey's armed forces have been dealt a significant psychological blow by the attempted coup, and their prestige and status have been damaged.
Turks had assumed that coups were a thing of the past.
Not only does this latest plot come as a threat to the country's democracy but it has also stymied its ability to act in its key role as a provider of regional security.
Reports on Tuesday said President Erdogan's Air Force adviser, Lt Col Erkan Kivrak, had been detained at a hotel in the southern province of Antalya.
According to Reuters news agency, 257 staff at Mr Yildirim's own office - some 10% of the total number - have also been removed from duty.
More than two dozen generals, including former air force chief Gen Akin Ozturk, have been remanded in custody pending the setting of trial dates.
Like Mr Gulen, Gen Ozturk denies any involvement.
Mr Yildirim said action would be taken against Mr Gulen's supporters.
"I'm sorry but this parallel terrorist organisation will no longer be an effective pawn for any country," Mr Yildirim said, according to Reuters.
"We will dig them up by their roots so that no clandestine terrorist organisation will have the nerve to betray our blessed people again."
Meanwhile, the UN urged Turkey to uphold the rule of law and defend human rights in its response to the attempted coup.
In a statement, High Commissioner for Human Rights Zeid Ra'ad Al Hussein said the mass suspension or removal of judges was "cause for serious alarm". He expressed "deep regret" at suggestions the death penalty could be reinstated.
According to official figures from the prime minister's office, Friday night's coup attempt left 232 people dead and 1,541 wounded.