http://www.bbc.co.uk/news/world-europe-18554246The F-4 Phantom disappeared over the Mediterranean, south-west of Hatay province, not far from Syria's coast.
PM Recep Tayyip Erdogan said initially that "the other side have expressed regret" but later was unable to confirm what had happened.
After an emergency security meeting, his office said it was understood that Syria had brought the plane down.
In a statement, it said a search for the two crew members was under way involving Turkish and Syrian coast guard ships. Once all the circumstances were established, it added that Turkey would respond decisively.
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Analysis
Jonathan Head
BBC News, Istanbul
Given the breakdown in relations between the two countries over the Syrian conflict, this incident has the potential to provoke a serious crisis. When gunfire from Syrian forces crossed the Turkish border earlier this year, Ankara threatened a military response.
Much will depend on whether or not the Turkish pilots have survived. If not, public anger might push the government into some kind of punitive action against Syria.
Syria's response will also influence Turkey's reaction. A clear apology, and a statement that the shooting was unintentional, might be enough to assuage Turkish anger.
But then again, we do not know yet whether the aircraft were clearly in Turkish airspace or not. Initial Turkish reports that they came down eight miles from Syrian territorial waters suggests that they were, but Syria may claim otherwise.
"Regarding our pilots, we do not have any information, but at the moment four of our gunboats and some Syrian gunboats are carrying out a joint search there," Mr Erdogan told reporters earlier on Friday evening.
I go for Syria. Turkey is overplaying its hand.