The Syrian military statement appeared on the state news agency
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 Turkey's Hatay province, near the Syrian coast.
The Turkish military said it lost radio contact with the F-4 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.
A Syrian 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 off the coast of Latakia province, 10km (six miles) from the village of Um al-Tuyour, he added.
"It later became clear the target was a Turkish military plane which had entered our airspace," he continued.
'Decisive response'
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.
Much will depend on whether or not the Turkish pilots have survived, our correspondent says.
If not, public anger might push the government into some kind of punitive action against Syria, he adds.
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.
Aleppo violence
Inside Syria, the violence continued on Thursday with state media reporting that "armed terrorist groups" had abducted and massacred 25 villagers in Aleppo province.
Activists said that rebels had shot dead 26 government supporters who were believed to be militiamen.
In Aleppo city, activists said a number of people died when security forces opened fire on a demonstration after Friday prayers.
Meanwhile, international envoy Kofi Annan has said it is time for the world to exert greater pressure to help bring the violence in Syria to an end.
Mr Annan called for Iran to be involved in attempts to end the violence, a proposal put forward by Russia but rejected by the US.
In a separate development, the BBC has learned that UK government officials have decided to prevent the head of the Syrian Olympic Committee, Gen Mowaffak Joumaa, from travelling to London for the Games.
The visa ban is believed to be linked to his relationship to President Bashar al-Assad's government.
