Abdullah Gul said Saturday that Turkey was still trying to establish the exact circumstances of the incident but conceded the jet may have strayed into Syrian air space.
Faruk Celik, Turkey's Labour and Social Security Minister, said Turkey would retaliate "either in the diplomatic field or give other types of response."
"Even if we assume that there was a violation of Syria's airspace — though the situation is still not clear — the Syrian response cannot be to bring down the plane," Celik told reporters on Saturday.
"The incident is unacceptable," he said. "Turkey cannot endure it in silence."
The incident further escalated tensions between the two neighbours, which used to be allies before the Syrian revolt began in March 2011. Turkey has become one of the strongest critics of the Syrian regime's brutal response to the country's uprising.
Turkish media say that Syrian and Turkish coast guards are conducting a joint search mission for the jet's two missing crew members on Saturday.
Late Friday, Syria's state-run news agency, SANA, said the military spotted an "unidentified aerial target" that was flying at a low altitude and at a high speed.
Syria said Friday its forces had shot down a Turkish military plane that entered its air space. The plane, an unarmed F-4, went down in the Mediterranean Sea about 13 kilometres from the Syrian town of Latakia, Turkey said.
Turkey issued a statement Friday night following a two-hour security meeting led by Turkish Prime Minister Recep Tayyip Erdogan, saying Syrian forces downed the plane and that the two Turkish pilots remain missing.
It said Turkey "will determinedly take necessary steps" in response, without saying what those actions would be.
"Following the evaluation of data provided by our related institutions and the findings of the joint search and rescue efforts with Syria, it is understood that our plane was downed by Syria," the statement said, without providing other details.
[h=3]A reconnaissance plane[/h]Turkish Foreign Minister Ahmet Davuoglu chaired a meeting Saturday with military officials during which they discussed possible steps and a search and rescue mission for the two missing pilots, the Foreign Ministry said. There was no announcement after the meeting.
Deputy Prime Minister Bulent Arinc insisted the plane was not a fighter jet but a reconnaissance plane and said Turkey was awaiting an explanation from Syria
Relations between Turkey and Syria were already tense before the downing of the F4 plane on Friday.
Turkey has joined nations such as the U.S. in saying that Syrian President Bashar Assad should step down because of the regime's brutal suppression of the uprising in his country. Turkey also has set up refugee camps on its border for more than 32,000 Syrians who have fled the fighting.
Syria and Turkey have expelled each other's ambassadors and Syria has accused Turkey of supporting Syrian opposition and even allowing Syrian rebels to operate out of Turkish soil. Turkey strongly denies the allegations.
After a cross-border shooting by Syrian forces in April, Turkey said it would not tolerate any action that it deemed violating its security. The firing had left two refugees dead at a camp near the town of Kilis just inside Turkey.
Foreign Ministry spokesman Selcuk Unal earlier on Friday rejected allegations that Turkey was sending arms and other equipment to Syrian rebels as baseless. Unal said Turkey was not sending weapons to any of its neighbours, including Syria.
Syria claimed the jet violated its air space over territorial waters, penetrating about one kilometre, but that Syrian vessels joined the search for it, according to Turkey's NTV television. It said Syria forces realized that it was a Turkish jet after firing at it.
