BEIRUT, Lebanon — Street names in Syria’s far northeastern corner have been changed from Arabic to Kurdish, schools openly teach the Kurdish language, and the country’s most powerful Kurdish militia flies its flag from checkpoints on main roads.

Across northeastern Syria, the Kurds, the country’s largest ethnic minority, have taken advantage of the vacuum left by the civil war to push for the autonomy long denied them by the government of President Bashar al-Assad.

Their struggle does not fit neatly into the war between Mr. Assad’s government and the rebels seeking his ouster, and different parts of the scattered Kurdish population have allied at times with forces on either side.

The fight for a measure of autonomy by Syria’s Kurds is the newest conflict in a broader struggle in which Kurds, spread across Turkey, Iraq, Syria and Iran and oppressed for decades, are trying to take advantage of the chaos in the Middle East to achieve longstanding ambitions for self-government and democratic rights. Most Kurds say their ultimate aim is an independent state, which was first promised to them, and then denied, by the victors of World War I. That perceived betrayal has sown deep grievances in the collective Kurdish psyche.