DAMASCUS, June 21 -- The U.S.-backed Syrian Democratic Forces (SDF) have killed over 300 militants with the Islamic State (IS) group and captured four neighborhoods in the Raqqa province over the past two weeks, the group said in a statement Wednesday.

Since unleashing their offensive on Raqqa almost two weeks ago, the SDF, which is a group of Arab, Kurdish and Assyrian fighters led by the Kurdish YPG, have captured the neighborhoods of Mashlab, Sbahiyeh, Romaniyeh and Sina'a in Raqqa city, as well as several areas in the countryside of that province.

In a statement, the group said they have killed 312 IS militants so far, and lost 15 of their comrades during the battle.

The aim of the U.S.-backed group is to fully liberate Raqqa from IS, which stormed the city and declared it as its capital in 2014.

Still, the operation in Raqqa sparked tension with the Syrian army, whose troops were advancing in the southern and western countryside of Raqqa.

The U.S.-led coalition shot down a Syrian war jet fighting IS in Raqqa recently, sparking tension with the Syrian army and the Russians, who said they suspended the safe flight agreement over Syria with the U.S. as an expression of rejection to the U.S. stance.

The U.S. said it was protecting the SDF from Syrian army's shelling, while the Syrian army said it was striking IS positions.

The SDF itself issued a statement recently, warning the Syrian army of further escalation, saying it will respond to any further attacks.