BEIRUT, Lebanon — The prospect of a wider war loomed over an increasingly chaotic battlefield in northern Syria on Monday, as fast-moving clashes pitted United States allies against one another and tensions grew between two major powers, Russia and Turkey.

Taking advantage of fierce Russian airstrikes, Kurdish-led forces advanced into shrinking rebel territory in the northern part of Aleppo Province, infuriating the insurgents and their principal backer, Turkey, which threatened “a severe response” if the Kurds moved farther.

The situation has pitted a dizzying array of warring parties against one another, illustrating how the enemy of my enemy is, as often as not, my enemy. Tensions have never been higher between Kurds and Syrian Arab rebels, who now accuse the Kurds of opportunistically attacking them in league with Russia and the Syrian government to advance their goal of seizing territory along the border with Turkey.

Those clashes are fueling a risky escalation of tensions, especially between Turkey and Russia. And they are pitting two American-backed groups against each other, since both the Kurds and many rebel groups in Aleppo receive American support.