Speaking at a joint news conference with Spanish Prime Minister Mariano Rajoy in Madrid on Thursday, Stoltenberg said: "Turkey suffered most from terrorist attacks over many years.”
“And Turkey, as all countries, has the right to self-defense,” he said.
Stoltenberg highlighted that this needed to be done “in a proportionate and measured way”.
“That is the message I convey every time I discuss this issue with different NATO leaders including the political leadership in Turkey.”
Turkey on Saturday launched Operation Olive Branch to remove PYD/PKK and Daesh terrorists from the city of Afrin.
According to the Turkish General Staff, the ongoing operation aims to establish security and stability along Turkey’s borders and the region as well as to protect Syrians from the oppression and cruelty of terrorists.
The operation is being carried out under the framework of Turkey’s rights based on international law, UN Security Council resolutions, its self-defense rights under the UN Charter and respect for Syria's territorial integrity, it said.
The military also said "utmost importance" is being put on not harming civilians.
Afrin has been a major hideout for the PYD/PKK since July 2012 when the regime of Syria’s Bashar al-Assad left the city to the terror group without putting up a fight.
Stoltenberg recalled his phone conversation with Turkish President Recep Tayyip Erdogan last week and urged for “direct contacts” between Turkey and the United States to find the best way to address the challenges in northern Syria.
The U.S. supports the PYD/PKK, considered by Ankara as the Syrian offshoot of the PKK terror organization that has waged a more than 30-year war against the Turkish state. The terror campaign has resulted in tens of thousands of deaths, including those of women and children.
American support for the terror group has long vexed Ankara as Washington views the PYD/PKK-led umbrella group, SDF, as a "reliable partner" in its fight against Daesh and continues to provide it with arms and equipment in the face of strong objections from Turkey.