Ankara's offensive on the Kurdish-held enclave in northwestern Syria is now in its 48th day as Erdogan vows to increase the operation beyond Afrin.
The US proposal to establish a permanent 30,000 strong force on the Turkish-Syrian border prompted the military offensive "Operation Olive Branch" to launch in the north of Syria earlier this year.
"Once we have purged the terrorists (from Afrin) we will then cleanse them from Manbij, Ayn al-Arab, Tal Abyad, Ra's al-Ayn and Qamishli", he said in televised comments.
Syria has slammed both Turkish and United States military activities on its soil as a violation of the Arab nation's sovereignty. The Turkish government views the YPG as a terror organization and the Syrian branch of the outlawed Kurdistan Workers' Party (PKK) militant group.
In his speech, Erdogan said the military operation would not end with the seizure of Afrin.
Erdogan has said his troops and the Syrian fighters they were backing could break into the town "at any moment", and on Saturday said they could go even further east.
The town of Manbij, east of Afrin, is considered a key flashpoint in any future conflict due to the U.S. military presence in the area.
Meanwhile, the NTV broadcaster reported that the Turkish Armed Forces had entered the central districts of Afrin together with the Free Syrian Army.
Abdel Rahman said that the advance sparked "major concerns" for tens of thousands of civilians in the town of Afrin.
Gubar fled to Nubl, a small city in northern Syria, which appears to be under the control of Assad regime but is actually occupied by Iran-backed armed groups.
According to the so-called Syrian Observatory for Human Rights, over one million civilians face an "unknown fate" as Turkey is laying siege to the region.
It says more than 200 civilians have also been killed, but Turkey denies the reports and says it takes the "utmost care" to avoid civilian casualties.
Yesterday Turkish soldiers captured the strategically significant area of Jinderes Hill after heavy clashes with the Kurdish militia.