Turkey will not hesitate to act if Syrian Kurdish militia, seen as a terrorist outfit by Ankara, do not leave the town of Manbij, the country's top National Security Council, MGK, said late on Wednesday.
President Recep Tayyip Erdogan has long threatened to expand Turkey's military operation into Manbij, after already taking control of the enclave of Afrin in Syria from the People's Protection Units (YPG).
Unlike Afrin, there is a US military presence in Manbij and any confrontation between the two NATO allies would mark a major escalation.
"It has been stated that terrorists in Manbij should leave the region immediately, otherwise Turkey will not hesitate to take the initiative there as it did in other regions," the MGK, which is chaired by Erdogan, said in a statement.
Ankara launched an air and ground offensive in Afrin in January to root out YPG fighters there.
Washington sees YPG as a key player in the fight against Islamic State jihadists.
On March 18, Turkish forces and their rebel allies took full control of Afrin, with the YPG largely withdrawing without a fight.
Manbij was once held by Islamic State (IS) jihadists before they were pushed out by Kurdish militia.
The US has repeatedly warned that Turkey's campaign in Afrin has risked distracting from the fight against IS.