A Turkish soldier shares a bottle of water with his comrade as they stand guard in Suruc, bordering with Syrian town of Kobani, Sanliurfa province, Turkey, June 27, 2015. Thomson Reuters

BEIRUT/KARKAMIS, Turkey — Turkish-backed forces pushed deeper into northern Syria on Monday and drew a rebuke from NATO ally the United States, which said it was concerned the battle for territory had shifted away from targeting Islamic State.

At the start of Turkey's now almost week-long cross-border offensive, Turkish tanks, artillery and warplanes provided Syrian rebel allies the firepower to capture swiftly the Syrian frontier town of Jarablus from Islamic State militants.

Since then, Turkish forces have mainly pushed into areas controlled by forces aligned to the Syrian Democratic Forces (SDF), a coalition that encompasses the Kurdish YPG militia and which has been backed by Washington to fight the jihadists.

A group monitoring the tangled, five-year-old conflict in Syria said 41 people were killed by Turkish air strikes as Turkish forces pushed south on Sunday. Turkey denied there were any civilian deaths, saying 25 Kurdish militants were killed.

"We want to make clear that we find these clashes - in areas where ISIL is not located - unacceptable and a source of deep concern," said Brett McGurk, U.S special envoy for the fight against Islamic State, using an acronym for the jihadists.

"We call on all armed actors to stand down," he wrote on his official Twitter account, citing a statement from the U.S. Department of Defense.

Turkey, which is battling a Kurdish insurgency on its soil, has said its campaign has a dual goal of "cleansing" the region of Islamic State and stopping Kurdish forces filling the void and extending the area they control near Turkey's border.

It has put Ankara at odds with Washington and adds to tensions when Turkey's government is still reeling from last month's failed coup, which it says Washington was too slow to condemn. U.S. Vice President Joe Biden sought to patch up ties in a visit last week, just as Turkish forces entered Syria.

In a news conference on Monday with a visiting European official, Turkish European Affairs Minister Omer Celik said: "No one has the right to tell us which terrorist organization we can fight against." He did not however mention the U.S. comments.

On Monday, Turkish-backed forces advanced on Manbij, a city about 30 km (20 miles) south of Turkey's border captured this month by the SDF with U.S. help. The thud of artillery was heard from the Turkish border town of Karkamis.

'Ethnic cleansing'

Part of the Turkish offensive involved re-taking the strategic city of Jarabulus from ISIS control. Southfront

SDF-aligned militia said they were reinforcing Manbij but insisted none of the troops in the region or the extra fighters heading to the city were from the Syrian Kurdish YPG militia.

Turkey has said its warplanes and artillery have bombarded positions held by the Kurdish YPG militia in recent days. It accuses the YPG of seeking to take territory where there has not traditionally been a strong Kurdish ethnic contingent.

"The YPG is engaged in ethnic cleansing, they are placing who they want to in those places," Turkish Foreign Minister Mevlut Cavusoglu said in Ankara, demanding Kurdish forces withdraw east of the Euphrates river, a natural boundary with areas of eastern Syria under Kurdish control.

The YPG, a powerful Syrian Kurdish militia in the SDF that Washington sees as a reliable ally against jihadists in the Syrian conflict, have dismissed the Turkish allegation and say any of its forces west of the Euphrates have long since left.

"Turkey's claims that it is fighting the YPG west of the Euphrates have no basis in truth and are merely flimsy pretexts to widen its occupation of Syrian land," Redur Xelil, chief spokesman for the Syrian Kurdish YPG militia, told Reuters.

U.S. Pentagon spokesman Peter Cook said the United States had demanded the YPG must cross back to the eastern side of the Euphrates but said Washington understood this had "largely occurred."

The Turkish offensive in Syria is known as Operation Euphrates Shield. Southfront

Turkey has not spelled out if it plans to set up a "buffer zone" in the region where it is fighting in north Syria. The region lies between two Kurdish-controlled cantons - one east of the Euphrates and the other to the west near the Mediterranean.

But Ankara fears that, if Kurdish militia create an unbroken swathe of territory, it could embolden the Kurdish militant PKK group which has fought a three-decade-long insurgency on Turkish soil to demand autonomy in Turkey's southeast.

On Monday, Turkey also launched air strikes on what it said were PKK targets in northern Iraq, a Kurdish-controlled region along another section of Turkey's southern border and where the PKK has bases.

Turkish-backed forces say they seized a string of villages south of Syria's Jarablus in a region controlled by groups aligned to the U.S.- and Kurdish-backed SDF. They also say they have taken a few places to the west in Islamic State areas.

The Syrian Observatory for Human Rights, which monitors Syria's conflict, said Turkish-backed rebels had seized at least 21 villages to the south and west of Jarablus since Aug. 25.

Syria's conflict began in 2011 as an uprising against President Bashar al-Assad. Since then it has drawn in regional states and world powers, with a proliferation of rival rebel groups, militias and jihadists adding to the complexity.

(Additional reporting by Tom Perry in Beirut, Orhan Coskun and Ece Toksabay in Ankara, and Can Sezer, David Dolan and Nick Tattersall in Istanbul; Writing by Edmund Blair; Editing by Nick Tattersall and Ralph Boulton)