Turkey is prepared to take its fight against Kurdish forces in northern Syria as far east as Iraq, President Recep Tayyip Erdogan has said.
Speaking in Ankara, Mr Erdogan reiterated that his forces will move against Kurdish-controlled Manbij, which risks confrontation with the US.
US troops are based in the city, which was taken from the Islamic State group (IS) by Kurdish-led forces in 2016.
Turkey launched its operation against the Kurdish militia last weekend.
Backed by pro-Turkish Syrian rebels, Turkish forces attacked the Kurdish enclave of Afrin with the declared aim of driving out the Kurdish People's Protection Units (YPG).
Turkey considers the YPG an extension of the banned Kurdistan Workers' Party (PKK), which has fought for Kurdish autonomy in south-eastern Turkey for three decades.
The campaign has strained relations between Ankara and Washington, which has supported the YPG in its fight against IS.
'Clean up Manbij'
The Turkish president told a meeting of his AK party that he was prepared to expand so-called Operation Olive Branch "until there is no terrorist on our border leading to Iraq".
He said that after Afrin was cleared, "we will, as promised, clean up Manbij of terrorists".
Manbij lies 100 km (60 miles) east of Afrin in YPG-controlled territory. The mainly Arab city is separated from Afrin by an enclave captured from IS by pro-Turkish rebels in a previous Turkish-led operation in 2016.
The US has had soldiers in Manbij since March 2017, when it dissuaded Turkey from attempting to take the city and got the YPG to agree to withdraw east of the River Euphrates.
However Turkey has complained such a move never happened.
Turkey's south-eastern border with Syria is its longest, stretching more than 870km (540 miles) from the Mediterranean in the west to Iraq in the east. About 700km of this border is controlled by the Kurds.
Ankara has long sought a buffer zone along the border and says its current operation will result in a 30km-deep "safe area" in the Afrin district.
Tensions between the US and Turkey - Nato allies - have soared since the start of the latest operation. Any Turkish offensive which expands into Kurdish-held territory further east will test the US, which has partnered with and equipped the YPG-led Syrian Democratic Forces (SDF) against IS for the past two and a half years.
Clashes meanwhile continued around Afrin on the seventh day of the Turkish campaign, though fighting has been less intense because of bad weather.
The UN has said about 5,000 people have been displaced so far by the clashes.
Turkey says 14 of its soldiers and allied rebels have been killed, while the UK-based Syrian Observatory for Human Rights (SOHR) says 58 pro-Turkish rebels and 53 SDF/YPG fighters have been killed.
Turkey put the number of Kurdish and pro-Kurdish fighters killed at over 300.