Members of Iraqi rapid response forces are pictured during clashes with Islamic State militants in Mosul, Iraq March 13, 2017. (Xinhua/Reuters Photo)

MOSUL, Iraq, March 13 (Xinhua) -- Iraqi forces on Monday liberated two neighborhoods from the Islamic State (IS) militants in the western side of Mosul, while the troops continued fighting fierce urban warfare in the old city center, the Iraqi military said.

The commandos of the Counter-Terrorism Service (CTS) completely freed the neighborhoods of Nafet and New Mosul in the western side of the city, locally known as the right bank of the Tigris River, which bisects Mosul, the Joint Operations Command (JOC) said in a statement.

The recapture of the two neighborhoods brought the CTS troops closer to the western edge of Mosul's densely populated old city center, where hundreds of thousands of civilians are believed to still be trapped under IS rule.

Also in the day, the federal police and Rapid Response brigades, the elite Interior Ministry units, are conducting clearing operations in the newly-freed Bab al-Toub neighborhood and adjacent areas from booby-trapped buildings, mines and terrorists hiding among the residents, a security source told Xinhua on condition of anonymity.

Meanwhile, progress by Rapid Response units was slowed by heavy street-to-street battles at the southern edge of the old city center, as snipers of both side topped many buildings at the lines of clashes in Bab-al-Toub neighborhood and nearby streets of Halab and Jamhoriyah, the source said.

Many of the old houses in the narrow alleys near the battle lines in the old city were demolished by sporadic suicide bomb attacks by IS militants and sometime by bombardment of international aircraft, the source added.

Iraqi Prime Minister Haider al-Abadi, who is also the commander-in-chief of the armed forces, announced the start of an offensive on Feb. 19 to drive extremist militants out of the western side of Mosul.

Late in January, Abadi declared the liberation of the eastern side of Mosul, or the left bank of Tigris, after more than 100 days of fighting against IS militants.

However, the western part of Mosul, with its narrow streets and a population of between 750,000 and 800,000, appears to be a bigger challenge to the Iraqi forces.

Mosul, 400 km north of the Iraqi capital of Baghdad, has been under IS control since June 2014, when government forces abandoned their weapons and fled, enabling IS militants to take control of parts of Iraq's northern and western regions.