Earlier, a new fire broke out in the mine in Soma, hindering the rescue teams. Yildiz said it had been extinguished and two more dead workers found.
He said the numbers added up with the missing persons' information provided by families.
"The newly discovered workers will be brought up and given back to their families," Yildiz said. "If there is no further demand to us and the information we have backs that up, then we will have finished our search work."
However, Yildiz confirmed that rescue teams would first conduct a final search throughout the mine before making a decision on ending the operation, four days after an initial fire sent deadly carbon monoxide coursing through it.
Turkey's worst industrial disaster triggered angry protests across the country aimed at mine owners accused of ignoring safety for profit, and also at Prime Minister Tayyip Erdogan's government.
He is seen as too close to industry bosses and insensitive in its reaction to the tragedy.
Erdogan has presided over a decade of rapid economic growth but worker safety standards have failed to keep pace, leaving Turkey with one of the world's worst industrial accident records.
The frustrations boiled over in Soma on Friday as riot police fired teargas and water cannon to disperse several thousand protesters.
Yesterday, demonstrators clashed with police in the western port city of Izmir, some setting up makeshift barricades and throwing stones and fireworks aimed at the police. Around 40 people were detained.
Meanwhile, there were also protests in Istanbul. Some residents in the city banged pots and pans from their windows, an act which was a feature of last summer's nationwide anti-government unrest.
The police intervention in Soma could add to public anger towards Erdogan.
The prime minister has survived mass demonstrations and a corruption probe into his government over the past year to remain Turkey's dominant politician.
However, Erdogan now risks alienating the conservative, working-class voters who form his party's base.
The operator of the mine, Soma Holding, has denied any negligence.