The first exchange happened shortly after intense fighting broke out across the border in Syria's Idlib province between Syrian rebels and regime forces, the private Dogan news agency reported.
A Turkish army unit based near Guvecci fired four 81 mm mortar shells in the first instance and two shells in the second, it said. No casualties were reported.
The Hatay governor's office indicated that the Syrian mortar had landed in Turkey accidentally, saying it was believed "to be have been fired by the forces of the Syrian Arab Republic at Syrian rebel groups on the Syrian side of the border."
The Britain-based Syrian Observatory for Human Rights said rebels had attacked army positions in the Syrian villages of Khirbet al-Jouz and Darkoush about 16 kilometers (10 miles) from Guvecci. Observatory director Rami Abdul-Rahman said both sides were exchanging mortar fire.
The Observatory added that rebels later took over Khirbet el-Jouz and were advancing toward army positions in nearby areas. It said dozens of soldiers were either killed or wounded while three rebels died in the fighting.
Relations between Turkey and Syria, once strong allies, deteriorated sharply after the uprising against Assad began in March last year. Turkey became one of the harshest critics of Assad's crackdown while Syria accused Ankara of aiding rebels.
Turkish Foreign Minister Ahmet Davutoglu told Turkey's state television TRT that "from now on whenever there is an attack on Turkey, it will be silenced."
Also Saturday, Assad made a rare public appearance when he laid a wreath at the country's Unknown Soldier statue in Damascus to mark the anniversary of the 1973 war with Israel, also known in Syria as the October War. Syrian state television broadcast the ceremony and likened the current crisis to the war with Israel.