Syria's Ministry of Foreign Affairs stated that Turkey's move was another violation of the country's sovereignty.
"The Syrian Arab Republic decisively condemns Turkish aggression against the town of Afrin, which is an inseparable part of Syria," the statement said, as quoted by the SANA news agency.
The Syrian government added that despite Turkey's claims Ankara had not informed Damascus of the military operation.
"Syria completely denies claims by the Turkish regime that it was informed of this military operation," a foreign ministry source told state news agency SANA.
On January 20, the Turkish Prime Minister Binali Yildirim said that the country's jets have bombed YPG, PYD targets in the Syrian city of Afrin.
"Out of 113 designated targets of the Democratic Union Party (PYD) Kurdish Syrian terrorist group, 108 have been destroyed as of 18:30 [15:30 GMT]. All the killed and wounded people, who have been sent to hospitals, are members of terrorist groups," the statement of the Turkish General Staff read.
According to the Anadolu news agency, aircraft hit a PYD observation post in Syria’s northern district of Afrin. Turkish F-16 jets have carried out strikes on six targets in Afrin, while the armed forces have launched artillery shelling from the Kilis province, bordering Syria, the Turkish Hurriyet newspaper reported.
Turkey's President Recep Tayyip Erdogan confirmed the beginning of the military operation in Afrin.
"The Afrin operation has de-facto been started on the ground," Erdogan said, adding that "this will be followed by Manbij."
The Turkish Foreign Ministry has said that Ankara notified Damascus and the United Nations about the progress of the military offensive in Afrin in writing.
"We are notifying the Syrian regime, as well as all other sides, including the United Nations, about the operation in written form," Cavusoglu said, as quoted by the NTV broadcaster.
Turkey has been threatening to launch an operation in Afrin since last week after the US announced it was going to start training a border security force composed of the Syrian Democratic Forces (SDF), affiliated with the Kurdish People's Protection Units (YPG), which Ankara considered as a terrorist group.