Sinam Mohamed, the chief envoy of the "Rojava self-ruled Democratic Administration" in the Kurdish-majority north of Syria, said she fears for her own family in Afrin.

Mohamed noted that Turkey is a NATO member and argued that the United States ought to be able to pressure its ally to halt an offensive that she said had so far mainly killed civilians.

"For us, the United States has a moral obligation to protect the democracy in this area, to protect the democratic system in this area," Mohamed told reporters in Washington.

For local leaders, the self-ruled area is an experiment in democratic federalism that could serve as an example for the rest of Syria as it emerges from an eight-year civil war.

But Turkey sees the Kurdish-led regions of northern Syria as a supply corridor for "terrorists" and a rear base for the PKK armed separatist movement it is fighting on home soil.

For the past four days Turkish forces and allied Syrian Arab fighters have been assaulting the Afrin canton, which is protected by the Kurdish forces of the YPG militia.

Mohamed insisted "not a single bullet" had been fired from Afrin towards Turkey and that if Turkey has a problem with the PKK it is a domestic issue and not a cross-border one.

The United States has worked with the Kurdish YPG, under the banner of the Syrian Democratic Forces (SDF) east of the Euphrates to fight the Islamic State jihadist group.

But the YPG in Afrin, west of the river, have no overt US backing and -- after Syria's ally Russia apparently gave Turkey the green light to attack -- they are under siege.