They have however ruled out going to war with Syria over the incedent.
An emergency meeting of NATO is currently underway to discuss the shooting, while the Turkish government say that the shooting, which they say happened inside Turkish airspace, was "hostile act by the Syrian authorities against Turkey's national security".
Syria meanwhile says they shot the F-4 Phantom jet down within their own airspace. The wreckage has not yet been found.
Turkey’s government have written a strongly worded letter to the UN Security Council called the shooting "a hostile act of the highest order", but they have not asked the Council for any action over the incident.
Deputy Prime Minister Bulent Arinc said, “We don't believe warmongering or provoking the crowds by being righteous is the right thing to do. What needs to be done will be done within a legal framework.”
Tensions rose further still yesterday when Turkey accused Syria of trying to shoot down another plane.
In further Syrian news, more heavy fighting has been reported in the beleaguered country. Rebel forces have reported fierce fighting near Republican Guard positions 8km (5 miles) from the centre of Damascus.