Turkish fighter jets responded in line with engagement rules, which changed in 2012 when Syria shot down a Turkish fighter jet, he said.
The Syrian government was yet to react to the Turkish military action. "How can Syria react to an action that they know is wrong?" Davutoglu asked.
Also, Turkish Defense Minister Ismet Yilmaz said Saturday that the Syrian helicopter entered seven miles (11.3 kilometers) into the Turkish airspace and remained in violation for five minutes before it was shot down at around 2 p.m. (11.00 GMT).
"I congratulate our armed forces who gave the due response to Syrian forces that breached our airspace," Yilmaz said in Sivas province. "Let our people be rest assured that our armed forces are on guard 24 hours a day to protect the rights of the Turkish nation."
In June 2012, Syrian forces shot down a Turkish fighter jet after it violated Syrian airspace, although Syrian forces issued it with no warning and the aircraft had already left Syrian airspace when it was targeted with missiles.
The incident prompted Ankara to announce that it was changing rules of engagement and would consider any approaching Syrian aircraft as a security threat and shoot them down.
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