Turkish President Recep Tayyip Erdogan repeatedly vows to "clean the region from this trouble completely", signaling that the offensive against PKK and the affiliated group will not remain merely with the operation in Afrin.
The city of Manbij, also held by the YPG, was captured from ISIS in a joint US-Kurdish offensive.
Ankara said it might also extend its aggression further east to Manbij unless the PYD/PKK leaves the strategically located city.
Turkish state media said Turkey's advance continued on Friday, with the forces now on the edge of the Afrin municipal district.
Earlier this month, Erdogan accused US President Donald Trump and his predecessor Barack Obama of failing to tell the truth over US support for the YPG.
He added that Turkey will help Afrin to rebuild and fix, including its electricity, water, education, and healthcare systems, just like it did in Jarablus, Ar-rai, Azaz and Al-Bab, after clearing these Syrian cities of Daesh terrorists during Turkey's Operation Euphrates Shield.More news: Ben Te'o promises England will bounce back against France in Six Nations
As part of the operation, 3,213 PYD/YPG/PKK and Daesh terrorists were neutralized, 42 soldiers were martyred and 202 soldiers were wounded, the statement added.
On Saturday, the Britain-based Syrian Observatory for Human Rights monitoring group said the Turkish forces were now four kilometres (2.5 miles) from Afrin town.
Turkish Foreign Minister Mevlüt Çavuşoğlu has announced time for completing the Olive Branch operation in the Syrian Afrin.
One of the neutralized terrorists was from the senior cadre of the PKK, it added.
In August 2016, Turkey began a unilateral military intervention in northern Syria, code-named Operation Euphrates Shield, sending tanks and warplanes across the border.
Turkey launched the operation in northern Syria on January 20 against the US-backed YPG in its border stronghold of Afrin in northwestern Syria.