The area around Manbij has been controlled since last year by the Manbij Military Council, a local militia that is a part of the Syrian Democratic Forces (SDF), an umbrella organisation of armed groups of which the YPG is also a part. YPG forces are believed to be now ensconced in Manbij and have the support of the United States.
U.S military vehicles and troops patrolled near Manbij on Saturday in an attempt to prevent tensions escalating between different forces taking on Islamic State.
Asked about a deployment of US forces near the northern city of Manbij, Syrian President Assad said: "Any foreign troops coming to Syria without our invitation ... are invaders."
Assad has said he saw promise in Trump's statements emphasising the battle against Islamic State in Syria, where US policy under President Barack Obama had backed some of the rebels fighting Assad and shunned him as an illegitimate leader.
WATCH: Russian forces stationed in Syria near the town of Manbij
"We haven't seen anything concrete yet regarding this rhetoric," Assad said in an interview with Chinese TV station Phoenix on Saturday.
"We have hopes that this administration in the United States is going to implement what we have heard," he said.
The United States is leading a coalition against Islamic State in Iraq and Syria. In Syria, it is working with an alliance of Kurdish and Arab militias. Their current focus is to encircle and ultimately capture Raqqa - Islamic State's base of operations in Syria.
This week, the US-led coalition announced that around 400 additional US forces had deployed to Syria to help with the Raqqa campaign and to prevent any clash between Turkey and Washington-allied Syrian militias that Ankara sees as a threat.
Asked about a deployment of US forces near the northern city of Manbij, Assad said: "Any foreign troops coming to Syria without our invitation ... are invaders."
"We don't think this is going to help".
Around 500 US forces are already in Syria in support of the campaign against Islamic State.
Assad said that "in theory" he still saw scope for cooperation with Trump, though practically nothing had happened in this regard. He dismissed the US-backed military campaign against Islamic State in Syria as "only a few raids", and said a more comprehensive approach was needed.
Assad noted that the Russian-backed Syrian army was now "very close" to Raqqa city after advancing to the western banks of the Euphrates River this week - a rapid gain that has brought it to the frontier of areas held by the US-backed forces.
He said Raqqa was "a priority for us", but indicated that there could also be a parallel army attack towards Deir al-Zor in the east, near the Iraqi border. Deir al-Zor province is almost completely controlled by Islamic State.
UN-led peace talks in Geneva ended earlier this month with no breakthrough.
Assad said he hadn't expected anything from Geneva.
