Also Saturday, Syrian Defense Minister Gen. Fahd Jassem al-Freij vowed to crush the rebellion and bring the violence that has engulfed the country to an end, The Associated Press reported.
The diplomatic crisis began on Wednesday, when a Syrian shell killed five civilians in a Turkish border town and triggered unprecedented artillery strikes by Turkey. Ankara has deployed more troops to its southern border with Syria, and has responded to each shell that has struck Turkish soil with its own artillery barrage.
On Friday, Turkish Prime Minister Recep Tayyip Erdogan cautioned Damascus not to test Turkey's "limits and determination" and said Ankara was not bluffing in saying it won't tolerate such acts.
Saturday's cross-border exchange began when two mortar shells fired from Syria landed in rural areas near the Turkish village of Guvecci, prompting Turkish return fire, Turkey's media reported.
Later Saturday, a third shell hit near another village in Turkey's Hatay province and Turkish troops fired back, the office of the provincial governor said.
No casualties were reported.
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 foreign-backed insurgents 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 foreign-backed insurgents uprising against President Bashar al-Assad began in March last year.
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.
Syria's defense minister said Saturday that the government is ready to give amnesty to rebels who repent and those who don't "will be crushed under the feet of our soldiers."
Al-Freij, who became defense minister in July after his predecessor was assassinated, also claimed that the government was getting the upper hand. "The most dangerous parts of the conspiracy have been passed and the killing is on its way to decline," he said.
The defense minister, who rarely makes public comments, spoke as Syrian troops launched a major offensive to retake rebel-held areas in the northern city of Aleppo, the central city of Homs and towns near the border with Lebanon.
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