Turkish military have returned fire to Syria in a tit-for-tat attack after a rocket and mortar shells hit a mosque near the border, injuring a Syrian woman.

The incident took place in the Yayladagi town, a Turkish province on the border with Syria, where clashes between Syrian troops and the Free Syrian Army intensified.

Three artillery shells fell in the Turkish countryside during battles between the rebel forces in Syria and forces loyal to President Bashar al-Assad for the control of the Armenian Christian village of Kasab.

A rocket hit the Haci Bilal mosque in central Yayladagi, which is sited across from a Syrian refugee camp. The mosque's wall partly collapsed injuring a 60-year-old Syrian refugee who was passing by.

"Our artillery troops have fired back at the region from where the shots originated," the Hatay governor's office said in a statement on its website.

Syrian government forces have intensified their shelling of positions seized by rebels in the coastal province of Latakia, focusing on the Kasab border crossing into Turkey.

The province, which is the historic homeland of President Bashar al-Assad's clan and his Alawite sect of Shiite Islam, was seized by opposition forces last week.

The Syrian Observatory for Human Rights said around 100 fighters had been killed on each side.

On Sunday, Turkey downed a Syrian jet that allegedly violated its airspace.

Damascus described the act as "a flagrant act of aggression".

But Turkish foreign minister Ahmet Davutoglu said his country was ready to take any measures against threats to national security.