According to Reuters, the Turkish army has been fortifying the 566 mile long border - stopping fighters and smugglers infiltrating Turkish towns.
Syrian opposition military group Ahrar al-Sham claimed it shot down the plane Saturday.
Yıldırım said it was not clear yet whether the plane crashed on Turkish or Syrian soil.
The crash comes as Turkey was forced to tighten its border this week with Syrian aggression escalating.
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Rescue teams have been dispatched to the area and it's believed the pilots ejected before the aircraft went down.
The governor noted that the situation was not a matter of border violation, and that the jet had not been engaged on the Turkish side. "We were looking for any injured people but were afraid to go near it in case it blew up", Polat said.
Syrian rebels in Idlib province downed a regime war plane on Saturday following what appears to be heavy anti-aircraft fire.
Turkey's state-run news agency Anadolu quoted a spokesman for the Islamist group Ahrar-al_sham, Ahmed Karaali, saying the regime plane was allegedly bombing Idlib province in northern Syria when it was shot down by the opposition forces.