ANKARA, Turkey -- The U.S. on Monday urged Turkish troops and Kurdish forces in northern Syria to halt their fighting, saying it hinders efforts to defeat the Islamic State group. But Turkey's president vowed to press ahead with the military operation until the IS and Kurdish Syrian fighters no longer pose a security threat to Ankara.

It was the first U.S. criticism of its NATO ally since it launched a U.S.-backed incursion into northern Syria to help Syrian rebels seize the town of Jarablus from the Islamic State group. They have been clashing with Kurdish Syrian forces around the town to try to halt their advance.

The battle now pits Turkey against the Kurdish-led force known as the Syria Democratic Forces-- a U.S.-backed proxy that is the most effective ground force battling IS militants in Syria's 5-year-old civil war. It puts Washington in the difficult spot of having to choose between two allies, and it is likely to divert resources from the fight against IS.

U.S. Defence Secretary Ash Carter said Washington has asked Turkey to "stay focused" on the fight against the Islamic State and not to engage with the SDF.

"We've called on both sides not to fight one another, not to fight each other," Carter said.

He told reporters at the Pentagon that Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, spoke to his Turkish counterpart Sunday. Carter added that he intends to discuss the issue next week in Europe with Turkish Defence Minister Fikri Isik.

Pentagon press secretary Peter Cook said the clashes were of "deep concern," adding that they were not co-ordinated with U.S. forces, "and we do not support them."

"Uncoordinated operations and manoeuvrs only provide room for ISIL to find sanctuary and continue planning attacks against Turkey, the SDF, the United States, and our partners around the world," the statement said.

Turkish officials responded by insisting that Kurdish forces "immediately" withdraw east of the Euphrates River or face more attacks by Turkish forces.

"No one has the right to tell Turkey to 'fight this terror organization but don't fight that terror organization,"' said Omer Celik, a Turkish cabinet minister.

Turkey's Hurriyet newspaper, in an online edition, quoted Deputy Prime Minister Numan Kurtulmus as responding to the Pentagon by saying the U.S. should keep to its promise and use its influence to press its Kurdish allies to withdraw to the east.

The sharp rhetoric -- and the continued fighting -- reflects the complicated and conflicting interests at stake in northern Syria after Turkish tanks rolled across the border Aug. 24 with the dual aim of containing the IS group and Kurdish forces.

The U.S. has supported Turkey in its demand that the SDF withdraw east of the Euphrates, which cuts into Jarablus. The goal is to clear the region south of Jarablus of Kurdish forces, thus keeping them from linking with other Kurdish-controlled areas in Afrin in Syria's northwestern corner.

Turkey pressed ahead with its offensive, seemingly bent on creating a de facto "safe zone" free of IS and the Kurds near its border. The Turkish military said Turkey-backed Syrian rebels -- a mix of various Islamist rebel factions -- have cleared 10 more villages of "terrorist entities" and now control of an area totalling some 400 square kilometres (about 150 square miles) south and west of Jarablus.

In an emailed statement, Turkish military officials said Syrian opposition forces were continuing their operations to clear IS-controlled areas.

Syrian opposition groups, meanwhile, reported that Turkish-backed Syrian rebels have captured more towns and villages as part of the operation named "Euphrates Shield," now in its sixth day.

Cook said the U.S. doesn't support reported Turkish airstrikes and artillery shelling of U.S.-backed Syrian Kurdish fighters -- or Kurdish attacks on Turkish troops -- in areas where IS fighters no longer operate.

In another sign of brewing discord, Cook said the Kurdish pullback to the east side of the Euphrates has "largely occurred."

Turkish President Recep Tayyip Erdogan said Turkish operations will continue "until terror organizations such as Daesh, the PKK and its Syrian arm, the YPG, cease to be threats for our citizens."

Daesh is the Arabic name for the Islamic State group; the PKK is the Kurdistan Workers' Party, which has waged a 30-year insurgency in Turkey; and the YPG is the main Syrian Kurdish force known as the People's Protection Units.

Earlier this month, the Kurdish-led Syria Democratic Forces crossed the Euphrates and drove IS militants out of Manbij, a key supply hub south of Jarablus, following a costly 10-week campaign.

"The SDF have proven to be a reliable and capable force, and our support for the SDF in its fight against ISIL is ongoing and will continue to do so," Cook said, using another acronym to refer to the Islamic State group. "They have fought hard and sacrificed to try and rid Syria of this hateful group."

The Jarablus Military Council, which is part of the SDF, said its fighters will withdraw to areas south of the Sajour River, a tributary of the Euphrates. The Sajour is north of Manbij.

"We declare the withdrawal of our forces to south, to the Sajour River, to preserve the lives of civilians and so that they (Turks and their allies) don't have any justification to continue shelling civilians," the council said.

The move is unlikely to be accepted by Turkey, since Ankara wants the rebels to withdraw completely east of the Euphrates.

Syrian opposition activists have said at least 35 civilians were killed in northern Syria in the Turkish-led operation so far. Turkey denied any civilians had been hit. A Turkish soldier was killed Saturday by a Kurdish rocket attack, the first such fatality in Turkey's ground offensive.

The Britain-based Syrian Observatory for Human Rights said the Turkey-backed rebels have captured 21 towns and villages near Jarablus from the Kurdish-dominated SDF.

The Observatory also reported clashes between rebels and IS fighters on the western edge of Jarablus. The Local Coordination Committees, an activist collective, said the rebels captured seven more villages since late Sunday.

Turkish artillery fired 61 rounds against 20 "terrorist" targets in and around Jarablus in the past 24 hours, Turkey's state-run Anadolu Agency reported.