That has set off a race to Deir al-Zour among an array of rival forces aiming to take control of the nearby border with Iraq.

Moving east from central Syria and the desert city of Palmyra are forces fighting for the government of President Bashar al-Assad, including Syrian Army troops and Iran-backed militias like Hezbollah. Moving north from rebel-held southern Syria are American-backed insurgent groups. The Syrian Democratic Forces attacking Raqqa also aim to continue southeast to the same area.

On Tuesday, the United States-led coalition also launched airstrikes directly against Syrian government forces for the second time in less than a month. The United States Central Command said that Syrian forces — more than 60 soldiers, with some armored vehicles and heavy weaponry — had breached the security zone around the base at Tanf in southeastern Syria near the Jordanian and Iraqi borders. American and British forces there are training Syrian opposition fighters to battle the Islamic State, and airstrikes were carried out under similar circumstances on May 18, officials said.

There were unconfirmed reports of new forces joining the fray in Raqqa Province too, with pro-government forces moving into the province from the east.

For now, though, the Raqqa offensive could take a long time, with a very high toll, judging from the protracted offensive in Iraq against the Islamic State’s other major urban stronghold, in Mosul.

Even with a victory, the aftermath of the Raqqa fight could be difficult, as well, with many residents fearful of the Kurdish militias involved in the attack. The Syrian Democratic Forces say they will hand power to a local council made up of Arab and Kurdish civilians, but in other places where they have done that, like the city of Manbij, many residents say the councils are a thin facade for the militias’ control.

The American military said in a statement that the fight for Raqqa would be “long and difficult” but that along with the Mosul battle, it would “deliver a decisive blow to the idea of ISIS as a physical caliphate.”