Manbij was seized in 2016 from Islamic State (IS) group by the Kurdish-led, US-backed Syrian Democratic Forces.
Erdogan's spokesperson said on Monday that U.S. military officials will come to Turkey this week to discuss coordination on Syria.
Turkey hasn't concealed its delight of Trump's decision as USA presence in northeastern Syria was always considered as a nuisance by Ankara.
Mayadin and Boukamal are to the north and south respectively, of the town of Hajin, which has seen fierce fighting and an increase in US and coalition airstrikes in recent weeks as USA -backed forces battle about 2,000 IS fighters who are clinging to the last sliver of the terror group's caliphate.
For weeks, Turkey has been threatening to launch a new offensive against the Kurdish fighters, who partnered with the United States to drive ISIS out of much of northern and eastern Syria.
Cavusoglu told Turkish media during a briefing that Ankara has "the power to neutralize [ISIS] alone" amid fears that a U.S. pull-out will hurt the fight against the militant group.
This is huge given that the complete US reversal in policy comes following a phone call last week between President Trump and Turkish President Recep Tayyip Erdogan, wherein Erdogan is reported to have pressed the Kurdish problem and presence of USA troops.
U.S. President Donald Trump tweeted Sunday about a telephone conversation he had with Turkish President Recep Tayyip Erdogan.
Kremlin spokesman Dmitry Peskov said there are no immediate plans for a meeting between the two leaders, Reuters reported. The remnants of the so-called Free Syrian Army, which never stopped complaining about what it saw as the West's reluctance to decapitate the Bashar al-Assad administration, are today allied with Turkey. He, however, warned that the movement "can lure many recruits mainly from Iraq and Syria". Pictures have emerged today showing Turkish armoured military vehicles and troop carriers being dispatched to the border with Syria. French ministers said in the aftermath of Trump's announcement that the fight against IS continued as the group had not been fully eliminated from the region.
The SDF has been Washington's main Syrian partner in the fight with Islamic State, but Turkey views the YPG fighters that form its backbone as a threat and has vowed to crush them.
"It is a sign of fear from the separatist terror organisation that it is using methods to sow confusion, but they have to know such tactics will not save them", Juma said. Since then, US -backed coalition forces have successfully rolled back almost all of the Islamic State's self-declared caliphate in Syria and Iraq, including the key cities of Raqqa and Mosul, which served as the group's main power centers.
It is widely believed that the reason for Mattis' departure is that Trump declined to retreat from his stand on withdrawal of all American troops from Syria.
"It doesn't mean that we gave up on our determination and operations we will launch against the YPG in the future", he said.
Turkey has repeatedly called on the USA to stop training and providing armed weapons to the YPG in the fight against ISIS, claiming that Turkish military forces would be more effective in eliminating the jihadist threat.