Reportedly, battles are also underway to liberate Maranez and Bafel heights.
The United States has around 2,000 military personnel in northern Syria supporting the so-called Syrian Democratic Forces (SDF), which is an alliance of militias in northern and eastern Syria and largely dominated by Kurdish People's Protection Units (YPG).
Turkish prime minister Binali Yildirim said the French president had a "flawed understanding" of Turkey's operations in Syria.
Manning said the US troops "do not operate with Kurdish forces in Afrin".
Turkey says seven of its soldiers have been killed. Turkey considers the Kurdish militia it is fighting in Syria an extension of the outlawed Kurdish rebels inside Turkey.
Turkish state-run news agency Anadolu reported yesterday that two villages in the Afrin region had been "cleared" of the YPG.
Rockets hit two houses and killed one 17-year-old and wounded another person, Anadolu said. Two of the victims were Syrian refugees.
Turkey's 12-day cross-border offensive against the Kurdish People's Protection Units (YPG), which Turkish President Recep Tayyip Erdogan last week threatened to expand, has strained relations with its North Atlantic Treaty Organisation allies.
As Turkey's military operation in Syria continues, officials in the US-led global coalition against Islamic State warned the offensive could destabilise recent gains against the extremists along the Iraq-Syria border in the Euphrates River valley.
French President Emmanuel Macron, in an interview with French daily Le Figaro, expressed his concern regarding the possibility of a Turkish "invasion" in the Kurdish enclave of Afrin, in Syria, as part of Turkey's recently launched military campaign there.