Turkey on Wednesday asked the United States to stop Kurdish fighters from travelling to Afrin to battle against Turkish troops.
The Turkish army on January 20 launched an operation against the People's Protection Units (YPG), a Kurdish militia deemed "terrorists" by Ankara.
The Pentagon said on Monday that Turkey's Afrin offensive caused an "operational pause" in their anti-ISIL activities.
"The US is expected to step in to stop YPG/PYD forces shifting - under US control - from Manbij to Afrin," Turkish presidential spokesman Ibrahim Kalin said in televised remarks.
"This is our most natural right. Whether they do it or not is a separate question but we have taken all the necessary measures on the ground," he added.
Washington, which has a military presence in Manbij - almost 100 kilometres to the east of Afrin - has been at loggerheads with Ankara over the YPG.
The YPG forms the bulk of the US-backed Syrian Democratic Forces (SDF) in the fight against ISIL.
At a news conference on Tuesday, the SDF announced it would pull fighters out of areas of eastern Syria, where they have been fighting pockets of ISIL fighters, in order to shore up defences in Afrin.
Ankara sees the YPG as the Syrian branch of the Kurdistan Workers Party (PKK), which for over three decades has waged an insurgency against the Turkish state and is banned by Turkey, the US and the European Union as a terror group.
US officials have said they will not get involved in the Afrin fighting and expressed concern it would detract from the SDF's operations against ISIL.