BEIRUT, Lebanon — Turkish forces and Turkish-backed militias appeared to have clashed with the Kurdish-led militia and its new allies, the Syrian government, in northeastern Syria on Thursday, raising the temperature in an already volatile area where multiple players are maneuvering for position after the abrupt pullout of American troops.

Turkish-backed forces pushed into several villages held by the Syrian Army, capturing one of them and causing an unspecified number of casualties, according to the Syrian government news agency.

The Turkish-backed militias’ advance also forced the Kurdish-led militia, the Syrian Democratic Forces, which was aligned with the United States until recently, to withdraw from several villages, according to the Syrian Observatory for Human Rights, a Britain-based war monitor.

Three S.D.F. fighters were killed in the battle, the group said on Thursday.

Fighting between the Kurdish-led forces and Turkey would violate the United States-brokered cease-fire that President Trump said this week had brought peace to the area. But fighters with the Turkish-backed militias, known as the Syrian National Army, denied attacking the villages on Thursday.