"There are over 70,000 appeals. This will take time, the mechanism has been set up at the ministries," Binali Yildirim told reporters in televised comments.
He said each request would be handled carefully, though he did not clarify whether they had come from the tens of thousands of people who have been detained, suspended from their jobs in the public sector or remanded in custody.
Ankara blames the July 15 coup bid on a rogue group in the military led by Muslim preacher Fethullah Gulen.
The Turkish government has responded to the coup with a vast crackdown to erase Gulen's influence from state institutions including the military, judiciary and education sector.
Some 32,000 suspects have been remanded in custody so far, according to government figures.