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.
A Syrian militant in the area told The Associated Press that the Russian pilot was shot and killed when he resisted capture.
Turkish presidential spokesman said Turkey will not tolerate the presence of a Syrian Kurdish militia "anywhere" along its southern border, hinting that Ankara might expand its military operation underway in the Syrian enclave of Afrin eastward.
Ankara says that major progress has been made in the 15-day operation, with nearly 900 YPG fighters killed so far although it is not possible to verify these figures.
To the east, Syrian troops and their allies captured the village of Tel Alloush, bringing them closer to the rebel stronghold of Saraqeb, according to the Observatory and the government-controlled Syrian Central Military Media.
Most of the civilians killed are Syrians displaced by conflict in other areas of the country, according to the PYD, the ruling political party in Rojava, northern Syria. The other Turkish soldier was killed in missile attack at border post in the southern province of Hatay's Kilis.
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One Turkish soldier was killed in clash with YPG militants in Syria's Afrin as part of the "Operation Olive Branch" which was started on January 20 to remove YPG and ISIL militants from the region.
Earlier on Saturday, the Turkish General Staff said one soldier had been martyred and another injured in Sheikh Haruz, where the terrorist group targeted a Turkish army tank.
Turkey has now lost 14 soldiers in fierce clashes during the offensive.
Kalin called on the United States to "disengage" from the YPG and said Turkey will continue communications with "our American allies to avoid any confrontation".
On Jan. 20, Turkey launched Operation Olive Branch along with the Free Syrian Army (FSA) to clear PYD/PKK and Daesh terrorists from Afrin, northwestern Syria. The YPG controls much of the territory along the border and an uninterrupted strip from Manbij to the Iraqi border.