IRBIL, Iraq: Iraqi forces made further gains in their offensive to dislodge Daesh (ISIS) from Tal Afar, seizing five more villages on the eastern and southern outskirts of the city, the military said Thursday. In the fifth day of their onslaught, Iraqi forces continued to encircle militants holding out in the city in far northwestern Iraq close to the Syrian border, according to statements from the Iraqi joint operations command. The spokesman for the U.S.-led coalition fighting Daesh in Iraq said Thursday the militants are “completely surrounded” in Tal Afar and “are being killed.”

U.S. Army Col. Ryan Dillon added that the Daesh militants in the town are being deprived of their resources and at the “cusp of yet another defeat.” Within the city limits, Iraqi forces captured three more neighborhoods – Al-Nour and Al-Moallameen in the east and Al-Wahda in the west, taking over several strategic buildings in the process.

The advances were the latest in the campaign to rout the militants from one of their last remaining strongholds in Iraq, three years after they seized wide swaths of the north and west in a shock offensive. Tuesday, the army and counterterrorism units broke into Tal Afar from the east and south.

The main forces taking part in the offensive are the Iraqi army, air force, federal police, the elite U.S.-trained Counter-Terrorism Service and some units from the Shiite Al-Hashd al-Shaabi, also known as Popular Mobilization, which began encircling the city Sunday.

About three quarters of Tal Afar remains under militant control including the Ottoman-era citadel at its center, according to an operational map published by the Iraqi military.

Located 80 km west of Mosul, Tal Afar lies along the supply route between that city – which Iraqi forces retook from Daesh in July after nine months of fighting – and Syria.

Tal Afar has produced some of Daesh’s most senior commanders and was cut off from the rest of Daesh-held territory in June.

Up to 2,000 battle-hardened militants remain in Tal Afar, according to U.S. and Iraqi military commanders. Between 10,000 and 40,000 civilians are estimated to be in the city and its surrounding villages.