Turkish and Syrian navies have conducted a joint search for Turkish airmen shot down by Syria over the Mediterranean.
Signals from both sides suggested neither wanted a military confrontation over yesterday's shooting down of the jet near their borders.
However, the joint operation will clearly sit uneasily, given the bitter hostility between the two former allies over Mr Assad's 16-month-old crackdown on opponents.
Turkey has declared it will respond decisively.
Turkish President Abdullah Gul said "It is not possible to cover over a thing like this. Whatever is necessary will no doubt be done,"
According to a Syrian military account, the Turkish plane was flying fast and low, just 1km off the Syrian coast when it was shot down.
It had been tracked at first as an unidentified aircraft and its Turkish origin established subsequently.
Earlier, UN Secretary-General Ban Ki-moon said that he hopes Turkey and Syria will exercise restraint over the incident.
The Turkish military has said that the fighter jet lost contact with one of its F-4 fighter jets off the southern Turkish coast near Syria.
The incident happened yesterday morning and Syria acknowledged that it had shot the plane down.
Separately, at least 30 people were reported to have been killed today by regime troops across Syria.
Rebel bastions were said to be shelled and clashes with opposition fighters were reported in several parts of the country.
Syrian President al-Assad has issued a decree forming a new government.
The new team consists of a new 35-member government, with 20 new faces, following the 7 May election.
Elsewhere in Syria, a Red Crescent volunteer was shot dead on first aid duty.
Bashar al-Youssef, 23, was shot in the head yesterday while wearing a uniform clearly marked with the Syrian Arab Red Crescent emblem.
Reports from Syria cannot be independently verified as state authorities have barred international journalists and rights groups.
