Ankara had called on the US to block the redeployment.
The US has backed the YPG-led Syrian Democratic Forces (SDF) as part of its campaign to eliminate the Islamic State. Turkey is furious with the US support for the SDF.
"Now our objective is Afrin... As of now, we have Afrin encircled. We can enter Afrin at any moment, God willing," Erdogan told his ruling party in Ankara, a day after Turkish forces took control of the town of Jandairis west of Afrin.
"The operations in Afrin will continue until this swamp of terror is dried," he warned.
On January 20, Ankara launched operation "Olive Branch" in the Afrin region of northern Syria against the Kurdish People's Protection Units (YPG) militia who control the area but Turkey regards as a terror group.
Despite encountering fierce resistance - which has seen 42 Turkish troops lose their lives - the Turkish military and its Syrian allies appear to have gained new momentum in the last weeks.
The capture of Jinderes on Thursday - one of the key centres in the region other than Afrin itself - was seen by analysts as giving Ankara a clear path towards its main target.
But the operation has ratcheted up tensions with the United States, pitting Turkey's army against a militia force allied with its fellow NATO member in the battle against Islamic State (IS) militants.
On Tuesday, Syrian militias allied with the Kurds said they would redeploy 1700 fighters from the frontlines against the Islamic State to the Afrin region.
Ankara had called on the US to block the redeployment.
The US has backed the YPG-led Syrian Democratic Forces (SDF) as part of its campaign to eliminate the Islamic State. Turkey is furious with the US support for the SDF.
Erdogan also reaffirmed his previous vows that Turkey would not limit itself to clearing the Afrin region of the YPG, saying it wanted to carry on to the town of Manbij to the east and then to the Iraqi border.
"Today we are in Afrin and tomorrow we will be in Manbij. And the next day we will ensure that terrorists are cleared east of the Euphrates River up to the Iraqi border," he said.
Manbij is regarded as a particularly delicate issue as the United States - unlike in Afrin - has a presence there, raising the prospect of a direct clash with Turkey.
On a visit to Ankara last month, US Secretary of State Rex Tillerson said that Turkey and the US had to solve the tensions surrounding Manbij as a "priority".