The Syrian military has said it shot down a Turkish plane "flying in airspace over Syrian waters", according to state-run news agency Sana.
"[The jet] was dealt with in accordance with the laws that govern such situations," a military spokesman said.
Turkey had earlier said it believed that one of its F-4 fighter jets had been shot down by Syrian forces.
A search for the two crew members is under way, involving Turkish and Syrian coast guard ships.
The F-4 Phantom disappeared over the Mediterranean, south-west of Hatay province, near the Syrian coast.
A military spokesman told Sana that an "unidentified target" had broached Syrian airspace from a westerly direction at 11:40 local time (08:40 GMT) on Friday.
The target was flying at high speed and at low altitude, the spokesman said.
Anti-aircraft defences had hit the plane with artillery, bringing it down in the sea 10km (6.2 miles) off the coast of Latakia province, he added.
"It later became clear the target was a Turkish military plane which had entered our airspace," he continued.
Earlier on Friday evening, Turkish Prime Minister Recep Tayyip Erdogan held a two-hour emergency meeting with his interior, defence and foreign ministers and the Chief of the General Staff, Gen Necdet Ozel.
Mr Erdogan's office said that Turkey would respond decisively once all the circumstances were established.
Given the breakdown in relations between the two countries over the Syrian conflict, this incident has the potential to provoke a serious crisis, the BBC's Jonathan Head in Istanbul reports.
Relations between Nato-member Turkey and Syria, once close allies, have deteriorated sharply since the uprising against Syrian President Bashar al-Assad began in March 2011.
Tens of thousands of Syrian refugees have fled the violence across the border into Turkey.