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The Syrian Democratic Forces (SDF) began its assault on Raqqa earlier this month after a long campaign to isolate Islamic State inside the city.
It took Qadisia, located in the west of Raqqa, after three days of intense fighting, it said in a statement on one of its official social media feeds.
The SDF has pushed Islamic State from swathes of northern Syria over the past 18 months. Turkey-backed Syrian rebels have also taken territory from it and the Syrian army has this year advanced rapidly against it in desert areas.
The U.S.-backed coalition has supported SDF advances against the jihadist group throughout the Raqqa campaign with artillery and air strikes, including some against Islamic State leaders.
This month, the coalition said its air strikes had killed Turki Binali, a Bahraini cleric who was the group's top religious authority and the most senior known Gulf Arab in Islamic State.
It also said last week it killed Fawaz al-Rawi, who it said was an important Islamic State financier, in an air strike in Syria.
However, coalition air raids have also caused large numbers of civilian casualties, according to the Syrian Observatory for Human Rights, a Britain-based war monitor.
It said on Saturday that coalition airstrikes in and around Raqqa had killed nearly 700 civilians so far this year. The coalition says it works hard to avoid killing civilians and investigates all reports that it has done so.