Syrian Kurdish leaders called on civilians Tuesday to take up arms to defend the Afrin enclave against a Turkish assault now in its fourth day.

Its spokesman Rezan Hedo told AFP: "It is an invitation for all Kurds in Syria to take up arms."

He said the Syrian Democratic Forces, a US-backed alliance dominated by the Kurdish People's Protection Units (YPG), was "ready to receive all those who wish to defend Afrin and provide them with weapons."

Afrin is one of three autonomous cantons the SDF has set up in areas under its control.

The other two -- Euphrates and Jazira -- are in the main contiguous area of SDF control further east.

Ankara announced the launch of Operation Olive Branch on Saturday after months of threatening to invade the Afrin enclave to dislodge the YPG.

It sees the militia as an offshoot of the outlawed Kurdistan Workers Party (PKK) which has waged a bloody insurgency in southeastern Turkey since 1984.

But the operation is hugely sensitive as Washington relied on the YPG to oust the Islamic State group from its strongholds in Syria and the Kurdish militia now holds much of the north.

US Defence Secretary Jim Mattis urged Turkey on Tuesday to "exercise restraint in the military action and the rhetoric."