The Turkish military earlier said it had lost contact with an F-4 Phantom over the Mediterranean Sea on Friday morning, south-west of Hatay province.
It did not confirm reports that Syrian air defense forces were responsible.
But local media are quoting Prime Minister Recep Tayyip Erdogan as saying “the other side has expressed regret”.
Recep Tayyip Erdogan also revealed that the two crew members were safe.
Relations between Turkey and Syria, once close allies, have deteriorated sharply since the uprising against Syrian President Bashar al-Assad began in March 2011.
The Turkish military said it lost radio contact with the F-4 at 11:58 local time on Friday while it was flying over Hatay, about 90 minutes after it took off from Erhac airbase in the province of Malatya, to the north-west.
“Search-and-rescue efforts have started immediately,” a statement said.
The private news channel, NTV, later cited unnamed military sources as saying that the plane had crashed off Hatay’s Mediterranean coast, in Syrian territorial waters, but that there had been no border violation.
The Turkish and Syrian coast guards were collaborating in the search for the two crew members and the plane, NTV reported.
Witnesses in the Syrian coastal city of Latakia meanwhile said Syrian air defenses had shot down an unidentified aircraft near the town of Ras al-Basit.
Lebanon’s al-Manar television channel – controlled by Lebanon’s Hezbollah Shia movement, an ally of the Syrian government – also reported that Syrian security sources had said that “Syrian air defenses shot down a Turkish warplane and hit another in Syrian airspace”.
There was no immediate confirmation from Turkish officials, but later it was announced that Recep Tayyip Erdogan would be holding an emergency meeting with his top military and intelligence chiefs to discuss the missing plane.
Recep Tayyip Erdogan was also said to have told Turkish reporters on a flight back from Brazil that “the other side have expressed regret” over the downing of the F-4, and also that the pilots had been recovered.
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