Syria has said it engaged the aircraft in its airspace “according to the laws that govern such situations”, and that it crashed into the Mediterranean Sea.
The Turkish and Syrian navies are searching for the two crew members.
Relations between Nato-member Turkey and Syria, once close allies, have deteriorated sharply since the uprising against Syrian President Bashar al-Assad began in March 2011.
More than 30 000 Syrian refugees have fled the violence across the border into Turkey.
After a cross-border shooting by Syrian security forces in April that left two refugees dead at a camp near the town of Kilis, Turkey said it would not tolerate any action that it deemed violating its security.
Gul said the Turkish government could not ignore the fact that Syria had shot down a Turkish aircraft.
“It is not possible to cover over a thing like this, whatever is necessary will be done,” he said.