(BBC) -- The civilians have fled communities near the border since Turkey launched an offensive to drive a Kurdish militia out of the Afrin region on Saturday.

Some are reported to have been prevented from crossing into territory controlled by the Syrian government.

The UN said it was ready to deliver aid to 50,000 people in Afrin if required.

World powers involved in the Syrian conflict meanwhile called on the Turkish military to exercise restraint because it risked exacerbating the country's humanitarian crisis.

Turkey's president has vowed to "crush" the People's Protection Units (YPG) militia, which controls Afrin and more than 400km (250 miles) of Syria's northern border.

He says it is an extension of the banned Kurdistan Workers' Party (PKK), which has fought for Kurdish autonomy in south-eastern Turkey for three decades.

The YPG denies any direct organisational links to the PKK - an assertion backed by the US, which has provided the militia and allied Arab fighters with weapons and air support to help them battle the jihadist group Isis in Syria.

Turkish troops and allied Syrian rebels so far appear to have made limited gains since the air and ground offensive began on Saturday.

On Tuesday, the Turkish state-run Anadolu news agency reported that rebels had captured the "strategic" village of Hammam in north-western Afrin, and had begun allowing civilians to return to eight already "liberated" villages and rural areas.

It also reported that a second Turkish soldier had been killed in clashes.

YPG sources told the Kurdish Hawar news agency that its fighters had foiled an attempt to seize the village of Qastal Jando, killing many attackers, and destroyed an armoured vehicle in Qoda.

Kurdish leaders also invited civilians to take up arms, saying the YPG was "ready to receive all those who wish to defend Afrin and provide them with weapons".

(Photo: reuters)