"Afrin will soon fall completely, with God's help," Turkish President Recep Tayyip Erdogan said in a speech. He added that he hopes it will happen by Wednesday night.
Addressing local officials in Ankara, Erdogan also said that civilians in the area had been evacuated through humanitarian corridors organized by Turkey.
Ankara launched an operation in northwestern Syria two months ago after the United States announced plans to bolster the SDF military's dominant force with training and weapons.
"We are controlling the nests of terrorism in northern Iraq. "Soon, we will strike very hard at the terrorists there."
Foreign Minister Mevlüt Çavuşoλουlu said last week that Turkey and the Iraqi central government could launch a joint military operation against Kurdish fighters following Iraq's May 2018 parliamentary elections.
Turkish warplanes regularly fire on the illegal Kurdish Workers' Party (PKK), which has camps in the mountains of northern Iraq near the border with Turkey.