Syrian rebels backed by the Turkish army took control of 11 villages from Kurdish-led forces in the north of the country in the past two days, while capturing only two new villages from Islamic State extremists, the Syrian Observatory for Human Rights reported Monday.

Turkey is now fighting a three-front war against Kurdish militants: on its own soil, in Syria and most recently in Iraq.

The escalation in fighting between Turkish forces and their rebel allies and the Kurdish-led fighters has sparked concern from the United States that the war against Islamic State, its top priority, could be negatively affected.

The state-run Anadolu news agency reported fresh airstrikes against the Kurdistan Workers' Party (PKK) in northern Iraq. Broadcaster CNN Turk quoted the Turkish military as saying it had struck 20 targets 61 times in Syria in the past 24 hours.

Also on Monday, rockets fired from Islamic State-held territory in Syria hit the Turkish border town of Kilis, injuring at least six people, a news report said.

The injured included two children, the DHA news agency reported.

Since January at least 20 people in Kilis have been killed by rocket fire.

Turkey says its operations in Syria are directed against both Islamic State and the Kurdish Democratic Union Party (PYD), which it regards as the Syrian branch of the PKK, Kurdish rebels operating on its soil.

The Kurds captured Minbij, south of where the current fighting is taking place, from Islamic State this month. But the strategic city now appears set to be captured again by Ankara's forces.

"We will continue our advance towards Minbij and its countryside and liberate it," a commander in the rebel Mutasim Brigade told dpa.

But the strength of the Turkish army, a NATO member, and the rebels has forced the Kurds to retreat southward along the Euphrates River.

Turkey - along with other rebel forces, including ethnic Turkmen fighters - last week launched an invasion of northern Syria, taking the border town of Jarabulus without significant Islamic State resistance and beginning strikes against the Kurds.

The Kurdish-aligned Jarabulus Military Council says its forces have withdrawn south of the Sajur river, nine kilometres from Minbij, "to protect the lives of civilians."

The Minbij victory by the PYD's fighters exacerbated Turkish and rebel fears that they would push further west to create a Kurdish entity along most of the Turkish border.

Turkish Foreign Minister Mevlut Cavusoglu said the PYD's armed wing, the People's Protection Units (YPG), will only be targeted if it remains on the western side of the Euphrates River, CNN Turk reported.

However, PYD co-chair Ayse Abdullah reported Turkish strikes and military moves near Kobane, a symbolic city east of the river on the Turkish border. Also, rebels have started an attack on YPG-held town near Aleppo, Kurdish sources said.

“We want to make clear that we find these clashes ... unacceptable and they are a source of deep concern,” Pentagon spokesman Peter Cook said of fighting in areas with no Islamic State presence.

"The United States was not involved in these activities, they were not coordinated with US forces, and we do not support them," Cook added in a statement. He urged de-escalation and talks, warning the fighting could give Islamic State a chance to counter strike.

The Islamic State-affiliated Aamaq news agency said Monday the group had taken two villages near Minbij, apparently capitalizing on the situation.

The US has supported the Kurdish forces in northern Syria since 2014 as part of Washington's search for ground troops to fight Islamic State. They have driven the extremist group from most of the Syrian side of the Turkish border.

While the US has said it won't back the Kurds in areas west of the Euphrates, data from the US-led coalition shows continued airstrikes against Islamic State in the Minbij area.

The US sees Islamic State as the focus of its strategy in Syria, where multiple wars are ongoing, including the main conflict between the government of President Bashar al-Assad and various rebel factions, among them hardline Islamist groups.

For much of the war, Turkey was focused on backing rebels fighting al-Assad, but is increasingly trying to ensure Kurdish gains are curtailed.

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