Last week, in a cafe in Kilis, a small Turkish city a few miles from the Syrian border, Lt. Col. Mohammed Hammadin was back for a few hours after leading an assault against Kurdish positions on a mountain south of the border. He is a former Syrian Army officer and a commander of the Levant Front, the largest faction of the Free Syrian Army.
Colonel Hammadin, 40, watched as a Free Syrian Army journalist shared video footage showing the colonel, still panting from his exertions, his hand on the shoulder of a captured Kurdish fighter.
He explained that his Syrian force shared aims with Turkey, first in wanting to see Mr. Assad go, but also in its dislike for the Kurdistan Workers’ Party, or P.K.K., which has waged a separatist insurgency for three decades against Turkey.
Like most members of the Syrian opposition in Turkey, the colonel described all the various Kurdish militant groups, no matter which side of the border they were on, as part of the same P.K.K. organization.
“Turkey has a right to attack the P.K.K. for its own national security,” he said. “It has the right to clear the area because the P.K.K. can attack its cities from the border.”
While he and his forces want Mr. Assad gone, they also want a united Syria. The Kurds, whose population straddles Turkey, Syria and Iraq, have long wanted to carve out their own nation.
“The most important reason to fight them is that they are separatists,” he said. “They want their own cantons on the northern border.”
The Kurdish militias had frequently sided with the Syrian government against the Free Syrian Army in the war, he said, helping enforce the siege of Aleppo, displacing Arab communities from their villages, and oppressing their own Kurdish people.
“They committed many violations,” he said. “They were very pragmatic to gain their own ends — an independent state.”
Syrians forced to flee to Turkey are bitter at the Kurdish militants. As such, the Free Syrian Army has embraced the Turkish fight against the Kurdish militants with gusto.
Free Syrian Army soldiers posted video on social media showing themselves heading to the border to join the Turkish operation. Syrian volunteers have flocked to a recruitment center in the town of Urfa to sign up.
“People are volunteering,” Colonel Hammadin said. “It’s good they want to apply, but our numbers are enough.”
Hunched over a coffee table in another part of Kilis, two Syrian brothers, Murshid and Bashar Sheikh Naif, explained why their family supported Turkey’s latest operation.
They had joined the uprising against the Assad government from the start in 2011. Murshid, 32, a former policeman, was imprisoned by the government for 18 months. He was released when the Free Syrian Army exchanged captured government soldiers for him.
Of eight brothers in the Naif family, five have joined the Free Syrian Army over the years. They have fought multiple enemies — first Syrian government troops, then Russian and Iranian forces, then extremists of the Islamic State, and now American-backed Kurdish militias, whom they blame for forcing them from their home.
Two brothers were killed, one fighting against the government and one against the Islamic State. Bashar, 22, was wounded fighting the Islamic State in an earlier operation alongside the Turkish Army. Two more brothers have joined the latest operation against the Kurdish militias in the enclave of Afrin, they said.
“We were neighbors,” the elder Mr. Naif said of the Kurdish fighters. “There were no problems until the S.D.F. became an enemy and pushed us out of our villages.”
The family fled to Turkey as the Kurdish militia seized their hometown, Tal Rifaat, and surrounding villages in 2016, he said.
He played a video on his cellphone showing the exodus of refugees — some 200,000 Arabs were displaced from a string of 15 villages and towns north of Aleppo — and their shelters in mud-soaked camps.
Their father died soon after, distraught at the loss of their home, Mr. Naif said. Their mother was dying of cancer, his younger brother added.
“So we have a common cause,” Mr. Naif said. “There is a common interest in fighting against the P.K.K. with Turkey. Turkey is our personal ally and they helped the people a lot.”
President Recep Tayyip Erdogan of Turkey gave the Free Syrian Army a strong endorsement in a speech on Tuesday, comparing them to Turkey’s National Forces, which fought for independence in the early 20th century.
“The Free Syrian Army is a civil formation, organized by people who gathered to protect their own country,” he said, addressing legislators from his Justice and Development Party. “We are happy to be side by side with our Syrian brothers in their freedom struggle.”
Nationalist support for the military campaign is running high in Turkey and dissent largely stifled. About 300 people, including members of the Turkish Medical Association, have been detained for expressing criticism of the operation on social media.
Some Syrian refugees in Turkey are confused as to what to think about Ankara’s decision to send tanks and planes into Syria.
Political and humanitarian activists voice fears that the operation will cause Syrians yet more civilian suffering, or stir strife between Kurdish and Arab communities in Syria.
Some warn that Syrian fighters are being used by foreign powers.
“Afrin is not our battle,” said an opposition activist, Yusuf Mousa. “As Syrians, we respect that Turkey is an ally of the Syrian revolution, but they are trying to make actions for their benefit.”
Yet while Turkey’s operation in Afrin has been cast as a narrow fight against Kurdish separatists, seizing the territory would boost the standing of the Free Syrian Army.
The group has steadily lost ground as an opposition force as the Syrian Democratic Forces, which the United States regards as its most effective partner in the fight against the Islamic State, have gained prominence.
With Turkey’s help, the Free Syrian Army wants to seize the northern countryside around Tal Rifaat and open a corridor to the northwestern province of Idlib, to rescue more than a million trapped civilians and fighters.
Mr. Erdogan has vowed to take control of a 20-mile zone along the length of Turkey’s border with Syria, and has called on United States forces to pull back from the Syrian town of Manbij.
Colonel Hammadin did not say how far his soldiers would go, but he ruled out any confrontation with American troops. He said he hoped for the United States’ support against Mr. Assad.
“America has the ability to do anything,” he said. “We look forward to them making the Assad regime leave.”