"The investigation is continuing, there are people who are being searched for. There could be new apprehensions, arrests and detentions," Yildirim said, according to the network's translation of his remarks.
"The process is not completed yet," he added.
Turkey issued arrest warrants Wednesday for 47 former staff of the Zaman newspaper as part of a sweeping crackdown since the attempted power grab on July 15.
More than 9,000 people have been placed in custody ahead of trial over the coup, which the authorities blame on reclusive US-based cleric Fethullah Gulen .
The prime minister also said Turkey was "determined" to secure Gulen's xtradition.
"We shared all the details with them and, from this point on, the task falls on the shoulders of the US government," the prime minister said.
Yildirim also said there were growing calls for a re-introduction of the death pentalty for alleged coup plotters that the government could not ignore.
"This is the only voice that we hear in all the squares," he was quoted as saying, adding: "Turkey is a democratic country, we are governed by democracy and there are requests of the nation.
"We cannot make this fall on deaf ears," he said.
Yildirim also spoke about relations with Russia in the interview, ahead of a visit by Turkish President Recep Tayyip Erdogan to the country next month.
"We will see more developed relations and that is what needs to take place," he said, adding: "We have... common interests, a common future".
Erdogan on August 9 plans to hold his first face-to-face meeting with Russian President Vladimir Putin since Moscow and Ankara mended ties damaged by the downing of a Russian jet last year.