The US defence secretary has called on Turkey and Kurdish forces in northern Syria to stay focused on fighting the Islamic State of Iraq and the Levant (ISIL) group and not to target each other.

Monday's statement by Ash Carter came after Turkish forces launched a two-pronged operation last week against ISIL, also known as ISIS, and Kurdish forces from the People's Protection Units (YPG) inside Syria.

Turkey said it killed 25 Kurdish "terrorists" in strikes on YPG positions on Sunday - meaning the two US-backed partner forces were fighting each other.

"We have called upon Turkey ... to stay focused on the fight against ISIL and not to engage Syrian Defence Forces (SDF), and we have had a number of contacts over the last several days," Carter said.

"We have called on both sides to not fight with one another, to continue to focus the fight on ISIL ... That is the basis of our cooperation with both of them - specifically not to engage."

The SDF is a group of fighters formed to fight against ISIL and is led by the YPG.

Turkish determination

Turkey said on Monday it would continue to target the YPG if it failed to retreat east of the Euphrates River.

Carter said the chairman of the joint chiefs of staff, General Joseph Dunford, had spoken to his Turkish counterpart on Sunday over the issue.

The US-led coalition has been backing the YPG with training and equipment to fight ISIL, while at the same time the US has also supported Syrian opposition groups fighting with the Turks in northern Syria.

Turkey regards the YPG as an extension of the outlawed Kurdistan Worker's Party (PKK), which has been battling the Turkish military for more than 40 years.

Peter Cook, Pentagon press secretary, also condemned the clashes in northern Syria.

"We want to make clear that we find these clashes unacceptable and they are a source of deep concern," Cook said on Monday, seconding Carter's call.

"This is an already crowded battle space. Accordingly, we are calling on all armed actors to stand down immediately and take appropriate measures to de-conflict."

In his remarks, Carter said: "The YPG elements of [the SDF] will withdraw, and is withdrawing, east of the Euphrates.

INTERACTIVE: Timeline of attacks in Turkey

"That will naturally separate them from Turkish forces that are heading down in the Jarablus area."

Turkish forces, backed by allied Syrian rebels, seized the town of Jarablus from ISIL last week, but also clashed with local fighters affiliated with the SDF.

In an interview published on Monday in the Turkish daily Hurriyet, Hulusi Akar, Turkish chief of staff, was quoted as saying that Kurdish forces around Jarablus have been attacking Turkish soldiers there.

"They have to withdraw to the east of Jarablus. Otherwise we will do what is necessary," he told Hurriyet.

On Monday, Turkish-backed Syrian rebels said they were advancing towards Manbij in northern Syria, a city captured earlier this month by Kurdish forces.