More than 50,000 people have been rounded up, sacked or suspended from their jobs by Turkey's government in the wake of last week's failed coup.
The government says they are allied to US-based cleric Fethullah Gulen, who denies claims he directed the uprising.
PM Binali Yildirim said the preacher led a "terrorist organisation".
"We will dig them up by their roots," he told parliament.
Turkey is pressing the US to extradite Mr Gulen and the issue was raised during a phone call between US President Barack Obama and President Erdogan on Tuesday, the White House said.
Spokesman Josh Earnest said a decision on whether or not to extradite would be made under a treaty between the two countries.
Read more:mTurkey coup attempt: Crackdown toll passes 50,000 - BBC News