A US-backed Kurdish militia has deployed fighters to the front line of Syria's Manbij to battle Turkey's military after President Recep Tayyip Erdogan said it would be next after launching the cross-border Afrin operation.

Manbij is about 100km east of Afrin where the United States has military personnel deployed in the fight against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS), meaning troops from the NATO allies could come face to face on the battlefield.

The US military coalition operating in Manbij said soldiers there have the right defend themselves against any attack, and wouldn't hesitate to do so.

"Clearly we are very alert to what is happening, specifically in the area of Manbij because that is where our ... coalition forces are," spokesman Colonel Ryan Dillon told Reuters news agency. "The coalition forces that are in that area have an inherent right to defend themselves and will do so if necessary."

Sharfan Darwish of the Manbij Military Council - a unit of the YPG Syrian-Kurd militia currently under attack by Turkey in Afrin - said his forces were preparing to confront Turkish soldiers.

"We are in full readiness to respond to any attack. Of course our coordination with the international coalition continues with regards to the protection of Manbij," said Darwish.

The intensifying situation in northern Syria led to a phone call between Erdogan and US President Donald Trump on Wednesday.

Trump expressed concern about Turkey's "destructive and false rhetoric" over the situation and urged caution so US and Turkish troops don't engage in battle.

"He urged Turkey to de-escalate, limit its military actions, and avoid civilian casualties and increases to displaced persons and refugees," a White House statement said.

"He urged Turkey to exercise caution and to avoid any actions that might risk conflict between Turkish and American forces."

Erdogan threatened earlier Wednesday to extend the Afrin offensive to Manbij to "clean our region from this trouble completely".

Decades-long uprising

Turkey sees the YPG - trained, armed and supported by the US to fight against ISIL - as an extension of the outlawed Kurdistan Workers Party (PKK), which has fought a bloody decades-long uprising in the country.

Erdogan indicated one aim of the anti-YPG operation was to create a safe zone where some of the more than three million Syrians who fled to Turkey in the civil war could return.

"First we will exterminate the terrorists, then we will make the area liveable. For who? For the 3.5 million Syrian guests in our land," Erdogan said.

Turkey's government has hit out at "propaganda" against its cross-border action. Erdogan's spokesman Ibrahim Kalin has urged the media and public to be aware of "fake, distortive and provocative news".

Meanwhile, rockets fired from northern Syria slammed into a mosque and a house on Wednesday inside Turkey, killing two people and wounding 11 others. The projectiles were fired in the early evening into the border province of Kilis.

One Syrian and one Turk were killed, the Kilis governor's office said, in attacks it blamed on the YPG militia in Syria.

The Turkish military said 260 Kurdish and ISIL fighters were killed so far in the five-day Afrin incursion - a claim refuted by a Kurdish commander who said the number was "greatly exaggerated".

Redur Xelil, an official from Syria Democratic Forces led by the YPG, denied the claim that ISIL fighters were involved in the fight for Afrin.