DAMASCUS, July 15 (Xinhua) -- The U.S.-backed Syrian Democratic Forces (SDF) have taken control of more than 42,000 square km of Syria, a monitor group said Saturday.

The SDF, an alliance of Kurdish, Arab and Assyrian fighters led by the Kurdish People's Protection Units (YPG), have expanded their control in several northern Syrian areas following battles with the Islamic State (IS) group.

Their recent notable gain was in the northern city of Raqqa, the main stronghold of the IS in Syria.

Syrian Observatory for Human Rights said despite the progress made by the SDF, the battles haven't reached the central part of Raqqa.

The London-based watchdog also said the battle of Raqqa is not easy, given the IS counter-offensives against the SDF.

The SDF announced the beginning of the battles to liberate Raqqa Province on Nov. 6, 2016, capturing areas in the countryside of Raqqa to isolate IS.

But June 6 this year marked the intrusion part of the battles into the heartland of IS in the city of Raqqa, which was self-declared by IS as its de facto capital in 2014.

Since then, the SDF succeeded to capture key areas on the western and eastern flanks of the city, and recently laid full siege to all exits and stormed the walls of the old city of Raqqa.