Erdogan made the announcement in a televised speech in the city of Kutahya on Saturday after Ankara started a de-facto ground operation in the northwestern border region of Afrin in Syria.
"The Afrin operation has de-facto been started on the ground," said Erdogan, adding, “This will be followed by Manbij.”
Meanwhile, Prime Minister Binali Yildirim said in a televised speech on Saturday that Turkish "armed forces have started an air campaign in order to destroy elements" of the YPG.
Reports said that Turkish fighter jets carried out 11 raids on the villages of Ain Dikneh, Mariamin, Tal Rif'at, Kafr Jannah, Maranaz and villages in the vicinity of Afrin in the northern countryside of Aleppo.
Afrin and Manbij are controlled by the YPG, which Ankara views as a terror organization and the Syrian branch of the outlawed Kurdish Workers’ Party (PKK).
Turkey has in recent days sent dozens of military vehicles and hundreds of troops to the border area. Over the past two days, Turkish forces have been shelling YPG targets around Afrin.
Turkey deployed troops to northern Syria in August 2016 without Damascus’ approval under the pretext of fighting the Takfiri terror group of Daesh. The operation, named Euphrates Shield, however, was later seen turning its focus on the Kurds, whom Turkey associates with anti-Ankara terrorists.
The operation ended last March, but Turkey recently redeployed its forces after the US announced a plan to set up a new 30,000-strong “border security” force, including the Kurdish militants, near the Turkish border. Washington had already angered Ankara by reneging on its promise of stopping its arms transfers to the Kurds and retrieving the weapons it had already given to them.
"The promises made to us over Manbij were not kept. So nobody can object if we do what is necessary," said Erdogan, referring to past American assurances that the YPG would move out of Afrin.
The Turkish president added that Ankara would "step by step" destroy a "terror corridor" that he said had been set up by the YPG.
"Later we will, step by step, clear our country up to the Iraqi border from this terror filth that is trying to besiege our country," said Erdogan.
Meanwhile, the so-called Syrian Democratic Forces (SDF), a US-backed group of mostly Kurdish militants, on Saturday accused Turkey of using cross-border shelling as a false pretext to launch an offensive in Syria.
The SDF, which controls swathes of north and east Syria, said it would have no choice but to defend itself if attacked.
Syria has censured both the American and Turkish plans for a fresh wave of unilateral military operations on its soil. Damascus views such measures as an assault on the country’s sovereignty.