Turkey's armed forces have shot down a Syrian plane after it crossed into Turkish air space in a border region where Syrian rebels have been battling President Bashar al-Assad's forces.

Turkish Prime Minister Tayyip Erdogan told supporters during a rally in Kocaeli that his country's armed forces had shot down the Syrian jet after it violated Turkish airspace, confirming media reports.

"A Syrian plane violated our airspace. Our F-16s took off and hit this plane," he told a rally of his supporters in northwest Turkey ahead of 30 March local elections.

"Why? Because if you violate my airspace, our slap after this will be hard."

Syrian rebels have been fighting for control of the Kasab crossing, the border region, since Friday, when they launched an offensive which Syrian authorities said was backed by Turkey's military.

Syria said Turkish air defences shot down the jet while it was attacking rebel forces inside Syrian territory, calling the move a "blatant aggression".

State television quoted a military source as saying the pilot managed to eject from the plane.

The Syrian Observatory for Human Rights monitoring group said initial reports from the area said the plane came down on the Syrian side of the border.

Al Manar, the television station of Assad's Lebanese ally Hezbollah, said two rockets had been fired from Turkish territory at the Syrian jet.