A UN official expressed concern over "disturbing reports" of civilian deaths and injuries during an ongoing military operation by Turkey against US-backed Kurdish fighters in northwestern Syria.

UN Regional Humanitarian Coordinator Panos Moumtzis also said on Sunday that civilians trying to flee the fighting in the area were being prevented "by local authorities" from escaping the violence.

Tens of thousands of people were now displaced in the Kurdish-controlled enclave of Afrin, while another 5,000 managed to reach surrounding villages and the city of Aleppo, he said in a statement.

"We continue to receive disturbing reports out of Afrin of civilian deaths and injuries, and restrictions on civilian movement as a result of ongoing military operations," said Moumtzis. "Those who risk moving continue to be stopped at exit points by local authorities in Afrin, preventing them from accessing safer areas."

On January 20, Turkey launched its operation to clear Kurdish People's Protection Units (YPG) fighters from its border in northern Syria. The military said on Sunday more than 2,660 "terrorists" had been "neutralised" since the offensive began.

The Turkish military said "only terror targets are being destroyed" and "utmost care" is being taken to avoid harming civilians.

Turkey, backed by allied Syrian militias, has gained ground in recent days against the Kurdish YPG militia.

The UK-based Syrian Observatory for Human Rights, which reports on the war using what it describes as a wide range of on-the-ground sources, said the advances threaten to encircle Afrin city, where one million people are estimated to live.

The Syrian Observatory said Turkish forces had advanced to within 12 kilometres of Afrin.

'Legitimate right'

Turkish forces seized the town of Rajo on Saturday, and Turkey's Prime Minister Binali Yildirim said they were advancing towards Afrin city "step by step".

He said on Sunday that fighting "terrorism" was the country's "most legitimate right.

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"Wherever the threat directed to our country comes from, that place is a target for us," Yildirim said in a speech in western Mugla province.

"We want peace in the region. We want brotherhood. We want tranquillity. We want the establishment of an environment of trust. That is what we are struggling for," he added.

Turkey has rejected international calls for it to suspend the Afrin assault in line with a UN ceasefire, which does not apply to the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), al-Qaeda and groups associated with it, or others deemed "terrorists" by the UN Security Council.

Turkey views YPG as an extension of the Kurdistan Workers' Party (PKK), which launched a decades-old fight against Ankara's rule.

The YPG has been an important ally for the US in the fight against ISIL.