"So nobody can object if we do what is necessary", said Erdogan, threatening to pursue the operations up to the Iraqi border. Stoltenberg said North Atlantic Treaty Organisation understood Turkey's concerns regarding the matter, the Daily Sabah newspaper reported.
"We will turn those plans to major victories for the people of the region, the Kurdish, Syrian, and Turkish people", YPG chief, Sipan Hemo pledged.
He said Turkey would continue to share the information with the actors in Syria.
Later on Saturday the Kurds accused the Turks of launching air strikes against residential areas in Afrin.
Turkish jets bombed the Kurdish-controlled city of Afrin in northern Syria on Saturday, as President Recep Tayyip Erdogan promised to expand Turkey's military border operations against a Kurdish group that has been the U.S.'s key Syria ally in the war on the Islamic State group.
On Friday, Turkish Defense Minister Nurettin Canikli said Turkey's operation in Afrin had "de facto" begun with cross-border shelling.
Erdogan said that after Afrin, the forces would also seek to oust the YPG from Manbij, a town to the east that the Kurdish militia also holds.
Turkey accuses the YPG of being a branch of the outlawed Kurdistan Workers' Party (PKK) that has waged an insurgency in its southeast since 1984.
But it was still unclear what form a Turkish ground operation will take amid considerable political and military risks.More news: Trump is behind Putin and Xi in the global popularity contest
Turkish military forces started an offensive today against the Afrin canton in northern Syria.
Moscow has been calling on the warring parties to exercise restraint.
"A full Turkish air and ground offensive will not take place without Moscow's blessing", said Anthony Skinner, director MENA at global risk consultancy Verisk Maplecroft, adding a full Turkish campaign is "not inevitable".
Some of their animus against the YPG comes from its having also fought Turkey-backed Arab Muslim guerrillas of a Muslim fundamentalist bent in Syria.
Ankara is fiercely opposed to the SDF, which is dominated by the Kurdish People's Protection Units (YPG) - considered by the Turkish government to be a "terrorist" group.
The Turkish Foreign Ministry is briefing the heads of missions of the United States, Russia and Iran in Turkey on the latest developments in Afrin, Anadolu reported.
The United States has continued to support the YPG in their fight against the Islamic State (ISIS/ISIL) despite Turkey repeatedly voicing concerns over the group's alleged ties to the terrorist PKK.
The Turkish attack comes after an announcement early this week by the Trump administration that it would arm and train a 30,000-man strong Kurdish force to police Syria's borders and make sure ISIL did not reemerge.
"Turkey is capable and determined to eliminate every kind of threat against it", Foreign Minister Mevlut Cavusoglu said on Twitter soon after receiving a call from U.S. Secretary of State Rex Tillerson.