Turkey's government has held an emergency security meeting amid reports that one of its fighter jets was shot down by Syrian security forces.
The F-4 Phantom disappeared over the Mediterranean, south-west of Hatay province, not far from Syria's coast.
Prime Minister Recep Tayyip Erdogan was initially quoted as saying: "The other side have expressed regret".
Later he could not confirm what brought the jet down but said rescue teams were searching for the crew.
"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," he said.
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 1158 (0858 GMT) 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.
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 Syrian coast guard was helping the Turkish coast guard, navy and air force search for the two crew members and the plane, NTV reported.
Witnesses in the Syrian coastal city of Latakia meanwhile told BBC Arabic that Syrian air defences had shot down an unidentified aircraft near the town of Ras al-Basit.
Lebanon's al-Manar television channel - controlled by Lebanon's Shia Hezbollah movement, an ally of the Syrian government - also reported that Syrian security sources had said that "Syrian air defences 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 Mr Erdogan would be holding an emergency meeting to discuss the incident with his interior, defence and foreign ministers and the Chief of the General Staff, Gen Necdet Ozel.
Mr Erdogan was also said to have told Turkish reporters on a flight back from Brazil on Friday afternoon that "the other side" had expressed regret over the downing of the F-4, and also that the pilots had been recovered.
But in his televised news conference on arrival at Ankara airport, he appeared to play down suggestions of an apology.
"I cannot confirm whether they have apologised or on what grounds they did so if they apologised," the Hurriyet website quoted him as saying.
Inside Syria, the violence has continued 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. A video has been posted online, purporting to show the bodies of some of the victims in the village of Darat Izza.
In Aleppo city, activists said a number of people died when security forces opened fire on a demonstration after Friday prayers.
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.
He was speaking in Geneva alongside the head of the UN observer mission, Maj-Gen Robert Mood, who suspended patrols in Syria at the weekend because of the risks to the safety of the 300 observers.
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.
The International Olympic Committee is expected to ratify the decision.