Kurdish-led fighters were approaching a strategic dam controlled by the Islamic State in northern Syria after days of fighting that killed a senior military commander of the extremist group, a spokesman for the U.S.-backed forces and others said Tuesday.

Talal Sillo of the Syrian Democratic Forces said the fighters, with the support of U.S., French and British special forces, have driven the Islamic State from dozens of villages and farms in recent days and were about three miles from the Euphrates Dam.

The SDF, a coalition of Kurdish and Arab fighters, has been on the offensive in Raqqa province since early November, advancing with the help of U.S.-led airstrikes. The operation is aimed at encircling and eventually retaking Raqqa, the de facto capital of the Islamic State’s self-declared caliphate.

The city is home to nearly 200,000 mostly Sunni Arabs and an estimated 5,000 Islamic State fighters.

“The ongoing operation is the second phase west of Raqqa,” Sillo said, adding that the first phase was north of the city. “More phases will come later to isolate the city and then to begin liberating it.”

The capture of the dam, which controls the flow of water to parts of Syria and neighboring Iraq, would deal a major blow to the extremist group, which has held the facility for more than two years. Behind the dam lies Lake Assad, which at 247 square miles is Syria’s largest reservoir.

Each side claims to have inflicted heavy casualties on the other. The Islamic State-linked Amaq news agency reported Monday that 24 SDF fighters were killed in the area, while Sillo said his forces had killed dozens of extremists.

The Britain-based Syrian Observatory for Human Rights said the fate of a top Islamic State military commander known as Abu Jandal al-Kuwaiti is still unknown after he was targeted by U.S.-led coalition aircraft. The Syrian army said Abu Jandal was killed fighting in the Tabqa area near the dam. Islamic State supporters on social media confirmed that he was killed.

The U.S. Central Command said coalition aircraft conducted nine strikes near Raqqa on Monday that engaged three Islamic State tactical units, destroying vehicles rigged with explosives, a bridge, a fighting position and a supply cache. It said two airstrikes near the Ein Issa area to the north of Raqqa hit two Islamic State tactical units and destroyed two fighting positions.

Sillo said that in recent days the SDF has captured 502 square miles. He said its next target is the town of Tabqa, home to a military base where Islamic State fighters killed scores of captured Syrian troops in 2014. He said the fighting on Tuesday was concentrated near the Jaabar castle on Lake Assad, after the SDF captured the nearby village of Jaabar.

The U.S.-backed SDF is made up of several Arab, Kurdish, Turkmen and Christian groups that have captured wide areas of northern Syria from the Islamic State over the past year. The largest and most powerful groups in the coalition are the main Kurdish militias known as the People’s Protection Units, or YPG, and the Women’s Protection Units, or YPJ.

The SDF is the most effective ground force battling the Islamic State in Syria.