In a later statement, it added a Turkish army tank had been hit in another attack, killing all five servicemen inside.
According to the Turkish side, the importance of Mount Darmak lies in its strategic position used to bomb the border city of Kalis with missiles fired by the Kurdish protection forces.
The statement said that since the beginning of the operation 13 Turkish soldiers had been martyred and 57 wounded.
Immediately after the attack at Sheikh Haruz, an air operation targeting terrorist shelters, hideouts and weapon emplacements in the area was launched at 5.52 p.m. local time (1452GMT).
Referring to Left Party members, Bystron said that they were "not concerned with stopping the armed conflict".
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Another soldier, the Turkish military said, was killed in clashes with the Kurdish forces.
Others described being detained, beaten and prevented from seeking medical attention, and said at least 10 people, including a child, were killed by fire from Turkish border guards. "There is not much to go", he said.
The suspect who was killed had entered Turkey illegally and received training from a branch of the Syrian Kurdish PYD group, the governor's office said.
Turkey's foreign and defense ministers on Saturday phoned the Anadolu Agency's correspondent who was injured in Friday's cross-border attack perpetrated by the terrorist PYD/PKK organization to inquire about his health.
Erdogan's spokesman Ibrahim Kalin meanwhile told journalists in Istanbul that the operation was going as planned but there was no timetable for its duration and it would "continue until we clear all those areas".