Following the announcement, US Defense Secretary James Mattis filed a resignation letter over his disagreement with US President Donald Trump on the latter's sudden decision to withdraw US forces from Syria.
'President @RT_Erdogan of Turkey has very strongly informed me that he will eradicate whatever is left of ISIS in Syria, ' Trump said in a Tweet around midnight Sunday, using another acronym for the militant group.
USA troops have been in Syria working with a Kurdish militia to fight the Islamic State terrorist organization.
A Turkish military column including trucks and armored personnel carriers as well as other carriers with armored vehicles, other material and ammunition entered the countryside of the Manbij area, the Syrian Observatory for Human Rights said.
The next day, Trump said Russia, Iran and Syria were unhappy about the US move "because now they will have to fight ISIS and others".
The state broadcaster broadcast video from the outskirts of Manbij, located on the western flank of the Euphrates River that splits northern Syria roughly into two halves.
The unexpected move has been widely criticized by many USA lawmakers who argued the action would undermine America's security and give away the region to Russia, Iran, and Syria.
Turkish Foreign Minister Mevlut Cavusoglu said on Saturday said no country would able to stop Turkey after the U.S. withdrawal from Syria, from eradicating the presence of the YPG/PKK.
For his part, Erdogan said in a Twitter post that two sides "agreed to increase our coordination on many issues, from trade relations to the developments in Syria". Mr Trump said on Sunday that the exit will be "slow" and "highly coordinated" with Turkey.
Turkey has long criticized the USA for training and arming the YPG, which it says is linked to domestic terrorists it has fought for more than three decades.
"I urge Trump to go back on his decision inciting Erdogan against the Syrian people in general and the Kurdish people in specific and I call on him to return the favour", she said.
Turkey has openly expressed an interest in attacking Kurdish forces in Syria, and Erdogan has previously threatened U.S. troops who were on the ground supporting the local fighters.
The Turkish president also wished a happy new year to the USA president and American people.
USA strategy to defeat ISIS relied primarily on training, equipping, and supporting Syrian Kurdish forces on the ground.
Last Wednesday, he had declared that Daesh was "beaten" in Syria and announced a stunning order to pull American ground forces from the war-ravaged nation.
Darwish dismissed the claims as "untrue", calling them "old accusations" from the rival Syrian groups.