HASAKAH, Syria – U.S.-allied Kurdish fighters have Syrian President Bashar Assad’s militias under siege in the northern Syrian city of Hasakah, and they are leaving them two options: “Surrender or die.”

In a conflict where alliances shift kaleidoscopically and the potential consequences of unwanted clashes are apocalyptic, this battle has raised the possibility Washington will be drawn into a direct conflict with the Syrian regime even as the Obama administration continues to focus its war effort on the forces of the so-called Islamic State, or ISIS.

The Americans’ key allies in the Syrian theater, the Kurdish People’s Protection Units, or YPG, are now very clearly fighting both ISIS and Assad. The lines of demarcation are increasingly hard to draw in Hasakah—and above it.

On Thursday, U.S. planes scrambled over the region when Syrian Air Force SU-24 attack planes launched strikes near the city.

A Defense Department spokesman, Navy Capt. Jeff Davis, suggested that “coalition personnel” were on the ground there. He did not get into specifics, but as we have reported previously, numerous American and European advisers are very close to the action in Syria.

“We view instances that place coalition personnel at risk with the utmost seriousness,” Davis added, “and we do have the inherent right of self-defense when U.S. forces are at risk.”

Davis said this is the first time U.S. planes have been scrambled in response to Syrian bombing, and pointed out that the coalition has never before seen the Assad regime take such action against the mainly Kurdish YPG.

Only a few days ago, these Kurdish forces—in alliance with some Arab contingents backed by U.S. airstrikes and supported by U.S. and other Western special forces—played a major role taking the strategic city of Manbijaway from the fighters of the so-called Islamic State.

Now very confident, seasoned, and well-armed, the Kurds appear about to achieve a victory not just over Assad’s beleaguered partisans in Hasakah, but by extension against his strategic backers from Iran, Lebanese Hezbollah—and Russia.

All the parties understand what a crucial turning point this represents.

Previously, the Assad regime and its supporters had acquiesced in the Kurdish operations against ISIS. Damascus was aware that the Kurds’ goal is to establish a federal autonomous (if not indeed independent from Damascus) region called Rojava along the northern Syrian frontier. That’s no secret.

But Damascus clearly thought it could address other threats first, putting its priority on crushing any remotely credible opposition, then perhaps turning on ISIS, which it initially helped foster, then taking care of the Kurdish problem one way or the other.

The Hasakah fighting has brought that tacit agreement to an end.

Moscow, hoping a deal might yet be made for a truce, sent a delegation last week to try to broker a ceasefire, but there was none to be had.

The Kurds now reject any form of agreement and demand regime forces leave the province of Hasakah altogether, giving the YPG and its political arm, the Democratic Union Party (PYD), complete control.

Note that Hasakah province is rich in oil and gas resources. Prior to the Syrian war, nearly half of Syria’s oil came from here. If Rojava is to survive, that oil and gas will be an important source of income, and the Kurds are not inclined to give it up.

The Assad regime “is increasingly weak and the regime’s external supporters have little ability to support the regime’s armed forces there,” Michael Stephens, the head of the Royal United Services Institute (RUSI) in Qatar, told The Daily Beast. And the events of the last couple of days would seem to bear that out.

When the Russian-brokered truce failed, even as the Syrian regime jets started to hit Kurdish positions and American or other coalition aircraft took to the air to warn them off, the Kurdish offensive continued.

Here in Hasakah, it’s clear the fighting between the YPG and the regime forces is much more intense than skirmishes in April. This time the battle has gone on for six days.

YPG officials say there are only a few pockets of Syrian government control left in a municipality that used to have a population of 200,000 people, and those holdouts are low on supplies.

“They used to say we are friends with the regime, but we are not a friend, we are supported by the people,” local commander Loqman told me before manning a heavy machine-gun on a pickup truck and blasting away at government positions.

On television Sunday, the exhausted-looking Syrian governor of Hasakah, Mohammad Za’al Ali, desperately pleaded with the Kurds to stop the fighting.

“Kurds in Hasakah are Syrians and cannot operate without the government,” he insisted on Kurdistan24, one of the few local TV stations operating in northern Syria. “Kurds cannot impose their control by force.”

But local commander Loqman said that the Kurds would not stop the fight. “What’s the job of the regime here? They have killed thousands of people, made millions of people homeless,” he said. “We should kick them out, that is my view.”

He also complained about the presence of foreign Shia militia fighters backed by Iran. These Syrian lands are his home, he said. “What is the work of Hezbollah here; what is the work of Russia here to kill civilians by airstrikes in Aleppo?”

In Hasakah’s dusty streets, local fighters wearing black scarves were keeping their heads down.

The town has a large Christian population, and one of the fighters, a Kurd with green eyes, wore a defiant white T-shirt: “Blasphemer,” it said. He also wore several crosses around his neck as he moved toward the front line. Christians fleeing the city center had given crucifixes to fighters, a local commander said.

Sniper fire is a major concern, and there’s a common belief the sharpshooters are foreigners.

“Iranian snipers hit civilians, no matter if they are Kurdish or Arabs,” says a 22-year-old Arab who goes by the pseudonym Adam. “There are Iranians, Afghans, Iraqis, Lebanese from Hezbollah, and the Iranian Revolutionary Guard,” he said, although I was not able to confirm this on this ground.

Dozens of Arabs from Hasakah and other towns have joined the Kurdish forces, but often won’t talk on the record for fear of government reprisals against their families in areas still controlled by the regime.

“I joined to protect our honor, because the Syrian regime is oppressing the people, killing civilians, and hitting them with airstrikes,” Adam said.

On Sunday afternoon there were no Syrian airstrikes and fighting slowed, with occasional sniper and heavy machine-gun fire. “From yesterday until now the airstrikes did not hit us,” said Loqman.

“The fighting stopped now because there are civilians; we must stop the war because there are civilians,” said Saydo, the other local commander, who speaks English. “But in the night the fight will begin again,” he said as we talked near the city’s central market.

Hussam Hassan, 50, a Kurdish civilian who was wearing a pink towel on his shoulders to deal with the sweat from the blazing heat, said he hoped to return to his house again soon.

“We flee because of the security,” he said near a Kurdish police checkpoint. “We are afraid, and I have children. There are airstrikes, artillery, and bullets.” He left by taxi to a village 15 kilometers away.

Sihanouk Dibo, a Kurdish official of the Democratic Union Party (PYD), accused the Syrian government of attacking the Kurds in agreement with Iran and Turkey, which opposes the declaration of a federal system for the Kurds and is hostile to the YPG/PYD, which is very closely allied with the insurgents of the Kurdistan Workers’ Party (PKK) operating inside Turkey.

“They don’t want a democratic federal region from Qamisli until Afrin,” Dibo said, referring to two major towns in northern Syria. They don’t want us to cut all the roads for terrorists,” Dibo said, noting that many ISIS recruits from abroad initially came into Syria through Turkey.

On Sunday evening, as predicted, heavy fighting resumed again in the city center and continues now, with the Kurds steadily advancing against Syrian government fighters.

“The regime has only a few points left, and is running out of water and food,” Ismael Resho, a YPG commander, told The Daily Beast.

The battle may be ending for now, but the kaleidoscope continues to turn, and the war goes on.