GAZIENTEP, Turkey — Clashes between Syrian rebels and Kurdish-aligned forces, both backed by the United States, intensified Sunday in northern Syria, as the rebels seized villages from the Kurds and Turkish warplanes pounded Kurdish positions, killing dozens.

The fresh fighting suggested that Turkey and its Syrian proxies are increasingly focused on stopping Kurdish forces from gaining more territory in northern Syria, particularly along Turkey’s border, potentially signaling a widening of the conflict.

Sunday’s clashes came a day after a rocket attack on two Turkish tanks killed a Turkish soldier and injured three others. Turkey, which is wrestling with Kurdish insurgents within its border, blamed the attack on Kurdish forces. They were Turkey’s first casualties since dispatching tanks and special forces units, backed by U.S. and Turkish fighter jets, into Syria on Wednesday to oust the Islamic State from the border town of Jarabulus.

The militants fled the town without putting up a fight. Since then, Syrian rebels have been pushing westward, chasing the Islamic State, as well as southward into areas controlled by forces aligned with the U.S.-backed Syrian Democratic Forces, or SDF. The SDF is largely dominated by the Syrian Kurdish People’s Protection Units, or the YPG, but also includes some Arabs.

On Sunday, pro-Turkey Syrian rebels of the U.S.-backed Free Syrian Army said they had wrested 10 villages from Kurdish control, while seizing four villages from the Islamic State, also known as ISIS.

Turkey’s state-run Anadolu news agency said Sunday that Turkish airstrikes killed 25 Kurdish “terrorists” and destroyed five buildings where the fighters were firing at advancing rebels.

The Syrian Observatory for Human Rights, a Britain-based monitoring group, said Turkish airstrikes and artillery shelling killed at least 20 civilians and wounded dozens during a fierce overnight battle for a village.

The increased tensions between the CIA and Pentagon-backed Syrian rebels and Kurdish forces threaten to take resources and attention away from the campaign against the Islamic State.

Targeting the Kurdish forces also could fuel friction with Washington, which views the SDF and the YPG as its most effective partners against the Islamic State.

The YPG’s senior command said that it was not engaging Turkish forces “despite the losses we suffer.” It added that “to stabilize the north of the country, the goal remains fighting Daesh and not Turkish forces,” using an Arabic acronym for the Islamic State.

Both Turkey and Syrian rebels say the YPG, as part of the SDF, has been targeting their forces. They say the Kurds broke a pledge to move their forces east of the Euphrates River, which senior American officials also demanded, and are pressing for more terrain. The YPG insists that it has pulled its forces back. What is clear, though, is that its SDF allies have not.

Shervan Derwish, a spokesman for a Kurdish-aligned military council in Manbij, said Sunday that the “battles are still ongoing.” At least 20 to 25 Turkish airstrikes have hit areas south of Jarabulus since Saturday, he said.