Turkey warned Monday it would carry out more strikes on a Syrian Kurdish militia if it failed to retreat beyond the Euphrates River, as Washington condemned their weekend clashes as "unacceptable".

Turkish forces pressed on with a two-pronged operation inside Syria against the Islamic State (IS) militants and the Syrian Kurdish People's Protection Units (YPG), shelling over a dozen targets.

But strikes against the YPG are hugely sensitive as the Kurdish group -- seen as a terror group by Ankara -- is an ally of Turkey's NATO ally, the United States, in the fight against IS in Syria.

Ankara said it had killed 25 Kurdish "terrorists" in strikes on YPG positions on Sunday, a day after a Turkish soldier was killed in a rocket attack allegedly by the militia.

The US envoy for the fight against IS, Brett McGurk, called the clashes "unacceptable" and urged an immediate de-escalation.

Turkey's operation aims to push the YPG back across the Euphrates River to prevent it joining up the region east of the river already under its control with a Kurdish-held area to the west.

US Vice President Joe Biden, visiting Ankara last week, said Washington had told the YPG to go back across the Euphrates or risk losing American support. But Ankara says it had seen no evidence of this.

"The YPG... needs to cross east of the Euphrates as soon as possible. So long as they don't, they will be a target," said Foreign Minister Mevlut Cavusoglu.

"In the places where it has moved, the YPG forces everyone out -- including Kurds -- who do not think like it does and carries out ethnic cleansing," he added.

Cavusoglu said the ethnic composition of the area around the city of Manbij west of the Euphrates -- captured by the YPG from IS earlier this month -- was largely Arab.

He said that those who had lived in the area before fighting broke out should be the ones who return and not new Kurdish migrants.

"But that is not the goal of the YPG," he said at a news conference alongside his Dutch counterpart Bert Koenders.

Cavusoglu also hailed the success of the lightning operation by Turkish-backed Syrian Arab fighters, who on Wednesday captured the town of Jarabulus from IS.

"As you see, even with a small force, the Daesh terrorist organisation is leaving and running away from the regions under their control," he added.

The Britain-based Syrian Observatory for Human Rights said at least 40 civilians were killed in Turkish shelling and air strikes on Sunday, claims that were strongly rejected by Ankara.

"Allegations that... civilians were shot at or targeted do not reflect the truth," the premier's office said, adding the army was taking "all necessary measures to prevent any harm to the civilian population".

It said 13 villages had "been cleared of terrorist elements" and were now controlled by anti-regime Syrian fighters that Ankara refers to as the Free Syrian Army (FSA).

Ankara-backed forces captured the IS border stronghold of Jarabulus last week, facing seemingly little resistance from the militants who fled to strongholds further south.

But the standoff with the Kurdish militia has been intense, with a Turkish soldier killed on Saturday in a YPG rocket attack on his tank.

McGurk wrote on Twitter that Washington was monitoring the reports of air strikes and clashes and found such fighting -- in an area clear of IS -- "unacceptable and a source of deep concern".

"The United States was not involved in these activities, they were not coordinated with US forces, and we do not support them," he said.

He called for steps to de-escalate the situation, adding that Washington was "actively engaged to facilitate such deconfliction" to keep the focus on the fight against IS.

NTV television said that in new action Monday the Turkish artillery had shelled 15 targets in northern Syria. It did not say which group was targeted.

Addressing a rally in the southern city of Gaziantep on Sunday, President Recep Tayyip Erdogan vowed to combat IS and the YPG "with the same determination."

Erdogan said Turkey's patience had run out after its border was repeatedly hit by IS rocket fire and 55 people were killed in a suicide bombing last weekend in Gaziantep.

Erdogan said the attack was carried out by a 14-year-old boy acting on the orders of the militants.