The US is willing to work with Turkey to address its legitimate security concerns in northern Syria, Secretary of State Rex Tillerson has said.
Turkish troops have seized a number of areas from Kurdish YPG control in recent days.
Turkey sees the group as terrorists, but they have been crucial in a US-led coalition against the Islamic State (IS) group.
Ankara said the US had to stop backing the YPG if they wanted cooperation.
“If they want cooperation, we are ready for this cooperation,” Turkey’s Deputy Prime Minister Bekir Bozdag said on Monday. “As the first step to take, they can stop arming terror groups and take back weapons already given.”
The YPG, or Kurdish People’s Protection Units, controls much of north-eastern Syria.
It is believed by Turkey to be an extension of the Kurdistan Workers Party (PKK), which has fought for Kurdish autonomy in Turkey for three decades. The YPG denies any direct links to the group.
Mr Tillerson said on Monday in London that the US recognised the country’s “legitimate concerns” for its security, and its right to defend itself from terrorist elements.
“We’re engaged with Turkey and we are engaged also with the leadership of our coalition and are asking that both sides show restraint,” he said.
He said the US had proposed measures to Turkey and others to try and stabilise the situation.
Reports say the US is discussing with Turkey and others the possibility of a “security zone” being set up in north-west Syria.
Earlier the Turkish President Recep Tayyip Erdogan vowed to not “step back” in the assault on the YPG enclave of Afrin.
“We are determined, Afrin will be sorted out,” Mr Erdogan said in a live television broadcast in Ankara on Monday.
“We will take no step back,” he said, adding: “We spoke about this with our Russian friends; we have an agreement.”
What has happened on the ground?
On Monday, the Afrin villages of Shankal, Qorne, Bali and Adah Manli were reportedly captured, along with rural areas including Kita, Kordo and Bibno, according to Turkey’s state-run Anadolu news agency.
But the Syrian Observatory for Human Rights (SOHR), a UK-based monitoring group, said the YPG had repelled Turkish troops from two villages that had been briefly captured in heavy fighting.
The YPG also said that it had retaliated against Turkey’s ground offensive with rocket fire on Turkish border areas. Two people died and 12 others were wounded when a rocket hit a camp housing Syrian rebel fighters near the border in Turkey’s Hatay province, local reports said.
The Syrian government, its ally Iran and Egypt have all condemned Turkey’s offensive.
What’s the background to the offensive?
Turkish ground troops, assisted by rebels from the Free Syrian Army (FSA), crossed into northern Syria on Sunday as part of “Operation Olive Branch” – an offensive to push out the YPG.
Turkish Prime Minister Binali Yildirim said the aim was to establish a 30km (19-mile) “safe zone” deep inside Syria and Mr Erdogan vowed to crush the YPG “very quickly”,
Plans for the operation are believed to have accelerated when US officials said earlier this month that it would help the Syrian Democratic Forces (SDF) alliance, which is dominated by the YPG, build a new “border security force” to prevent the return of IS.
Some 25,000 pro-Turkey fighters have joined the offensive, rebel commander Maj Yasser Abdul Rahim told Reuters. It is not clear how many Turkish soldiers are on the ground.
What are the casualties?
The SOHR said on Monday that 54 combatants had been killed since Saturday, including 26 Kurdish fighters and 19 pro-Turkish rebels. Twenty-four civilians had also died, it added – 22 in Turkish air and artillery strikes, and two as a result of Kurdish fire.
The Kurdish ANHA news agency reported earlier that at least 17 civilians have been killed in Turkish attacks.
Turkish Foreign Minister Mevlut Cavusoglu has denied killing civilians, and accused the YPG of emanating “nonsense propaganda and baseless lies”.
Turkey also says that none of its soldiers have been killed or injured in the operation so far.
However, ANHA said dozens of Turkish troops and Syrian rebels had been killed or wounded in YPG counter-attacks on Monday alone.
How have the key players reacted?
Western powers, including the UK and France, have urged restraint in order to avoid civilian casualties.
The UN Security Council has been meeting to discuss the Turkish ground offensive, as well as the wider humanitarian situation in Syria,
The French ambassador to the United Nations, François Delattre, said council members shared the view that Turkey should act with restraint. Mr Delattre would not say if Turkey ought to stop the operation altogether.
In earlier reaction:
- Syrian President Bashar al-Assad condemned the incursion, saying: “The brutal Turkish aggression” on Afrin was part of Ankara’s policy of “support for terrorism” in Syria
- Russia – a key ally of President Assad – also said it was concerned by the news, and withdrew some of its troops based in the area
- Iran, another Syria ally, called for a quick end to the operation “to prevent a deepening of the crisis” in Syria.
- The European Union’s diplomatic chief Federica Mogherini said she was “extremely worried” by the offensive