Turkey suspended over 2,500 more staff from the powerful religious affairs state agency on Tuesday in the latest purge after last month's failed coup blamed on US-based Islamic preacher Fethullah Gulen.

The religious affairs directorate, Diyanet, said in a statement that 2,560 people have been suspended in the latest wave, bringing the total dismissed to 3,672 since July 15.

Diyanet, which is directly linked to the prime minister's office, was established in 1924 to control religion in officially secular modern Turkey.

The agency has a budget larger than many ministries including health and takes care of close to 80,000 mosques in the predominantly Muslim country.

It has 100,000 personnel including imams but Diyanet did not give details of those dismissed.

Diyanet said "the commission created for this purpose (to find Gulen sympathisers) continued its rigorous work".

The reclusive cleric is accused by Ankara of ordering the coup in which a rogue military faction tried to oust President Recep Tayyip Erdogan from power without success.

Gulen, who is the leader of the Hizmet "service" movement, strongly denies the accusations and his lawyer said on Friday Turkey had failed to provide "a scintilla" of proof to support its claims.

Since July 15, tens of thousands of people from the military, judiciary, civil service and education suspected of links with the movement have been dismissed from their jobs or detained.

Justice Minister Bekir Bozdag said on Tuesday around 16,000 had already been remanded in custody ahead of trial while another 6,000 people were in detention awaiting initial court hearings.

Prime Minister Binali Yildirim said 25,000 new teachers and police officers would be employed after the purge to fill gaps created in state institutions.