"We can enter it at any moment", said Erdogan at the inauguration of the governing Justice and Development (AK) Party's Politics Academy in capital Ankara. "The next day we will ensure that the east of Euphrates will be cleared of terrorists up to the Iraqi border", he said.
"Right now, Afrin city centre is surrounded".
The monitor says at least 370 YPG fighters and 340 rebel fighters have died since the assault began.
Turkish soldiers and warplanes have made significant advances in the countryside of the border region of northwest Syria since launching an offensive in January that put Turkey at odds with its worldwide partners.
Turkey regards the YPG as a terror group and a branch of militants in Turkey who have waged an insurgency for decades.
Turkish authorities often use the word "neutralized" to imply the terrorists in question either surrendered or were killed or captured.
Erdogan noted that a total of 815 square kilometres (506 square miles) have been cleared from the terrorists so far.
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"By May, the operation in Afrin will come to an end", Çavuşoğlu is quoted as saying by Turkish media.
The Turkish postal service or PTT is now serving a Syrian city liberated from terrorists in 2016 by Turkish soldiers.
Operation Olive Branch is Turkey's second major military intervention in Syria during the unprecedented foreign-backed militancy that broke out in 2011.
Turkey is now engaged in a cross-border offensive in Syria to drive out Kurdish fighters it considers to be an extension of the PKK.
Turkey ended its campaign in northern Syria in March 2017 but at the time did not rule out the possibility of yet another military offensive inside the Arab country.