BAZWAYA, Iraq -- Iraqi forces reached a position within firing range of the Islamic State of Iraq and Syria (ISIS)-held city of Mosul on Monday, a military source told CBS News.

Iraqi special forces were advancing on Mosul early Monday. Moving in from the east under heavy fire, they were inching closer to the city’s limits.

The elite unit paused its advance last week. It had made ground quicker than other units, and wanted to allow forces on other fronts to make further progress.

Car bombers were trying to stop the advance, but the troops, just 2 miles from Mosul’s eastern outskirts, aimed to enter it later in the day, Brig. Gen. Haider Fadhil said.

Get Breaking News Delivered to Your Inbox

The dawn assault saw armored vehicles, including Abrams tanks, move on the village of Bazwaya as allied artillery and airstrikes hit ISIS positions, drawing mortar and small arms fire.

For two weeks, Iraqi forces and their Kurdish allies, Sunni tribesmen and Shiite militias have been converging on Mosul from all directions to drive ISIS from Iraq’s second largest city. The operation is expected to take weeks, if not months.

Since the offensive began on Oct. 17, Iraqi forces moving toward the city have made uneven progress. Advances have been slower in the south, with government forces there still 20 miles from the city.

The U.S. military estimates ISIS has 3,000 to 5,000 fighters inside Mosul and another 1,500-2,500 in the city’s outer defensive belt. The total number includes around 1,000 foreign fighters.

A day earlier, thousands of fighters flocked to join Iraq’s state-sanctioned, Iran-backed Shiite militias who are to cut off Mosul from the west. In a series of apparent retaliation attacks, suicide bombers on Sunday struck in Baghdad’s mostly Shiite neighborhoods, killing at least 17 people.

The deadliest of the bombings, a parked car bomb, hit a popular fruit and vegetable market near a school in the northwestern Hurriyah area, killing at least 10 and wounding 34. On Monday, ISIS issued a statement claiming responsibility for the attack.