He said that no matter who ended up governing Syria after the war, the Kurds would protect their gains.
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.
But for now Kurdish leaders say their goal is more autonomy within existing countries, with Kurdistan in Iraq as a model.
Recently, Kurdish assertiveness in Syria has set off rounds of clashes, pitting Kurds against rebel groups that accuse them of collaborating with Mr. Assad, and against fighters linked to Al Qaeda who see Kurdish control as a challenge to their plan to establish an Islamic state.
Scores of fighters from both sides have been killed, and new violence is shaking Kurdish areas long considered quiet. This week, a car bomb killed a prominent Kurdish politician, Isa Huso, in Qamishli, and rebel forces took over a Kurdish village in Aleppo Province, detaining about 200 Kurds, activists said.
The fighting highlights the further shattering of battle lines in the Syrian civil war as rebel groups focus their efforts on local struggles only loosely connected to their declared goal of toppling Mr. Assad.
Kurdish political leaders say they are not seeking an independent Kurdish state in northern Syria, but are only pushing for greater Kurdish rights. They model their struggle in part on the status achieved by Kurds in Iraq, who run a region in the north that is essentially independent from Baghdad, conducting its own foreign policy, controlling its ports of entry and fielding its own armed forces.
Although for now that region relies on Iraq’s central government for much of its budget, it has sought deals with Turkey and foreign companies to sell its oil in a bid for economic independence. Meanwhile, Syrian Kurdish militiamen have traveled to Iraqi Kurdistan for training, and the Kurdistan Workers’ Party, or P.K.K., which is negotiating its own peace with Turkey, has provided support to its brethren in Syria.
A recent trip by a reporter through the Kurdish area of Syria revealed many steps toward Kurdish autonomy as well as fighters who have taken up arms to obtain it.
“The Kurds will take their right to self-determination under any political regime, with President Assad or without him,” said Haval Mahmud, a militiaman with the Democratic Union Party, known by its Kurdish-language abbreviation, P.Y.D., in Qamishli. “We are gaining our rights with our blood, not as a gift from any side.”
About 9 percent of Syria’s 22 million people are ethnic Kurds, most of them living in communities scattered near the Turkish border, with greater concentrations to the east, near Iraq.
They have long complained of discrimination by the state, which suppressed their language and invested little in their areas despite the region’s richness in oil and agricultural land.
While many Kurdish youths joined the anti-Assad uprising that started in 2011, Kurdish political parties mostly charted a neutral path, feeling that neither side had much to offer.
But since the uprising became a civil war and the government withdrew from many isolated areas, Kurdish militias have filled the void in their communities.
Turkish leaders worry that a strengthened P.Y.D., which is linked to the P.K.K., could embolden its Turkish counterpart or lead to cross-border attacks.
The head of the P.Y.D., Saleh Muslim, sought to reassure Turkish officials during a visit last week to Ankara, the capital, that his group would establish only temporary administrations in its areas.
Turkey’s foreign minister, Ahmet Davutoglu, praised Mr. Muslim’s approach, while Prime Minister Recep Tayyip Erdogan warned against any “wrong and dangerous steps” toward Kurdish autonomy in Syria.
Recent visits to Kurdish areas in northern Syria revealed that the P.Y.D. is the strongest Kurdish force on the ground and that it has formed a patchwork of local alliances to defend its areas, teaming up with Arab tribes in some places while reaching accommodations with the government in others.
“The P.Y.D. is a pragmatic party that has its own project to administer Syria’s Kurd-populated areas, establishing political, social, cultural and security institutions,” said Maria Fantappie, a researcher with the International Crisis Group who has studied Syria’s Kurds. “This is their project, and we can expect them to make all the alliances they need as a temporary compromise.”
The recent spike in violence has pitted P.Y.D. militias against rebels and fighters from two extremist groups with links to Al Qaeda: Al Nusra Front and the Islamist State in Iraq and Syria.
In mid-July, clashes broke out between the two sides in Ras al-Ain in Hasaka Province, and Kurdish fighters quickly seized control of the ethnically mixed town with help from the local Arab tribes that distrust the extremist groups.
“We are Sunni Muslims, but this is not Afghanistan,” said an Arab resident, Hajj Omar, 50. “I am a Sunni Muslim, I pray five times a day, my sons pray, my wife is covered and we observe all the Islamic rituals, but we cannot live under these radical Islamic groups.”
Since then, clashes have spread throughout the ethnically mixed region along the border, with each side erecting checkpoints to control roads and kidnapping civilians to put pressure on its foes.
After Kurdish fighters failed to seize the mixed town of Tal Abyad farther west along the border, extremist fighters blew up a Kurdish administrative building and the homes of Kurds believed to be supporting the fighters, activists said.
“They don’t want to finish the Assad regime like we do,” said a rebel fighter who goes by Abu Abdul-Rahman, 30. “They want to establish their own independent state.”
The largest Kurdish stronghold is the eastern city of Qamishli, near the border with Iraq, an ethnically mixed city with a large Kurdish population.
The government withdrew its forces from the city center last year, leaving only a contingent at the airport and allowing the P.Y.D. to take over.
At a checkpoint near the city’s southern edge, Mr. Mahmud, the P.Y.D. fighter, denied that his group received support from the Syrian government, recalling its decades of neglect of Kurds.
“A new government will be established to fill the gap until the end of the Syrian crisis,” he said, near a poster of the jailed P.K.K. leader Abdullah Ocalan. He said that no matter who ended up governing Syria after the war, the Kurds would protect their gains.
“Surely, the clock will not be turned back,” he said.
Ben Hubbard reported from Beirut, and an employee of The New York Times from Qamishli, Syria. Tim Arango contributed reporting from Baghdad, and Sebnem Arsu from Istanbul.