The United States has pledged to stop supplying weapons to Kurdish militia in Syria, Turkey says, calling on Washington to immediately remove its troops from a Syrian town of Manbij that Turkish forces plan to target next.

US National Security Adviser HR McMaster told Turkish President Tayyip Erdogan spokesman, Ibrahim Kalin, that the United States would no longer provide weapons to the Kurdish YPG militia, the Turkish presidency said.

Turkey's air and ground offensive in northwest Syria's Afrin region against the Kurdish YPG militia has opened a new front in the seven-year, multi-sided Syrian civil war and strained ties with NATO ally Washington.

Turkey has criticised the United States for arming YPG. ( Reuters: Rodi Said )

Ankara views the YPG as terrorists and as an extension of the outlawed Kurdistan Workers Party (PKK) and has been infuriated by US support, including arms and training, for the militia.

Kurdish fighters have played a prominent role in US-led efforts to combat the hard-line Islamic State in Syria.

When Turkey launched their attack on the city of Afrin last week, Kurdish forces called on their US ally for help, while NATO ally Turkey warned against US involvement.

"The US and international community have a moral obligation to stand behind the Kurdish people now," YPG forces said in a statement as the offensive began.

Just prior to the launch of the eight-day-old incursion, dubbed "Operation Olive Branch" by Ankara, Mr Erdogan criticised the US for arming the Kurds, saying, "this is not what allies do".

Mr Erdogan said he hoped the US "would not give rise to error by appearing on the same side as the terror organisation".

Turkey 'challenging US position'

Guney Yildiz — Syria and Kurdish specialist for the European Council for Foreign Relations — told the ABC Turkey chose to begin its attack with Afrin because the US does not have airspace control or troops in that area.

Sorry, this video has expired Kurds ask Syrian government for help fighting Turkish forces

But Mr Erdogan's announcement of plans to attack Manbij, where the US do have troops, and to then push right through to the Iraqi border was a "challenge the US position", Mr Yildiz said.

Earlier in the week, the White House warned that the campaign risked exacerbating a humanitarian crisis and disrupting what had been a stable area.

Mr Erdogan said he hoped the US would not side with the Kurds, who he views as a "terror organisation". ( AP: Kayhan Ozer )

"We urge Turkey to exercise restraint in its military actions and rhetoric, ensure that its operations are limited in scope and duration, ensure humanitarian aid continues and avoid civilian casualties," White House spokeswoman Sarah Sanders said in a briefing.

The agreement to stop supplying weapons is likely to be seen by Ankara as a substantial diplomatic victory from the incursion, where Turkish troops and their Syrian rebel allies appear to have made modest advances.

Turkey's foreign minister said the United States needed to follow up its promise with concrete action, including the immediate withdrawal of its troops from the vicinity of Manbij.

"The United States needs to break its link with [the] terrorist organisation and make them drop their weapons completely," Mevlut Cavusoglu told reporters.

"They need to collect the weapons they gave, they need to withdraw from Manbij immediately."

The United States has about 2,000 troops in Syria, officially as part of the international coalition against Islamic State.

Sorry, this video has expired Turkish ground forces enter Syria to deal with Kurdish militia ( Middle-east correspondent Matt Brown )

ABC/Reuters