"They and their collaborationists may go into some individual actions, assassinations. They may attempt to cyber attack," Numan Kurtulmus said during a live broadcast on the Haberturk television channel.
"We need to be on the alert from now on. The state is on the alert with its all departments. It is cautious to get rid of all kind of possible threats in future," he said, adding that there are currently 216 fugitive soldiers.
All state departments should be cleared of individuals who have ties to the Fetullah Terror Organization (FETO), according to Kurtulmus.
Turkey's government has said the July 15 coup attempt, which left 240 people martyred and nearly 2,200 injured, was organized by followers of Fetullah Gulen, who has lived in self-imposed exile in the U.S. state of Pennsylvania since 1999, and his Fetullah Terrorist Organization.
Gulen is accused of leading a long-running campaign to overthrow the state through the infiltration of Turkish institutions, particularly the military, police and judiciary, forming what is commonly known as the parallel state.