In the meantime, Turkey has been working to strengthen its military position both along the Syrian border and by proxy forces already inside the country.
The foreign minister also criticised the French president, Emmanuel Macron, who has said French forces will remain in Kurdish-held Syria as a buffer.
According to AA sources, 40 pickup trucks, two tanks, several lorries and armored personnel carriers entered Manbij from the south.
The spokesperson for the Kurdish-led Manbij Military Council, Sharfan Darwish, said Turkish reinforcements have arrived in the area.
Donald Trump's move to withdraw U.S. troops from Syria prompts speculation on whether Turkish President Recep Tayyip Erdogan blackmailed his United States counterpart into the decision, according to Wesley Clark, a former North Atlantic Treaty Organisation commander.
Trump announced plans last week to withdraw roughly 2,000 US troops from Syria following a phone call with Erdoğan on December 14 in which the two leaders agreed on the need for more effective coordination on the war-torn country.
Major players in and around Syria have started positioning their forces as discussions get under way on how to proceed once US forces vacate the country and their fight against the last remnants of the Islamic State terror group's self-proclaimed caliphate.
Turkey has previously launched two operations with the rebels in Syria against IS in August 2016 and against the YPG in its northwestern enclave of Afrin in January 2018.
Canada mounting global effort to free Canadians detained in China
The detainee, Sarah McIver from Alberta, Canada , is under administrative detention by Chinese police due to working illegally. The Huawei official was arrested after the U-S requested her extradition allegedly for violating anti-Iran sanctions.
Also Sunday, French President Emmanuel Macron said he "deeply regrets" Trump's decision to pull US troops out of Syria and warned it could have risky consequences. After many years they are coming home.
Differences over Syria have always been a source of tension between the United States and Turkey.
United States forces are still in Manbij and the Turkish-backed fighters will not advance until they withdraw, Hamoud told Reuters.
The U.S. has since 2014 partnered with the Syrian Kurdish militia to drive out ISIS, a partnership that soured relations between Ankara and Washington. They are preparing to take Manbij first, he said.
Turkish and USA troops began joint patrols in Manbij on November 1 as part of an agreement that focuses on the withdrawal of YPG/PKK terrorists from the city to stabilize the region.
Youssef Hammoud, spokesperson for the Syrian opposition fighters, accused the USA -backed Kurdish militia of reaching out to the Syrian government to replace US troops if they withdraw. The future of the global coalition against IS, which includes Turkey, the USA and France, remains unclear.
Critics say thousands of IS members are still in Syria and could pose a threat with some analysts concerned the withdrawal could lead to a resurgence of IS.
The Syrian Observatory for Human Rights said the reinforcements were sent to the front line with Manbij, where US troops have been based. "The SDF is fighting against the terrorism that fomented attacks against Paris and elsewhere".