The Kurdish-led Syrian Democratic Forces said the operation will continue "until all the city is cleansed from terrorists who refused to surrender."
The SDF has been on the offensive in Raqqa since early June and now controls about 90 percent of the city that was once the extremist group's self-styled capital.
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The operation was named after Adnan Abu Amjad, an Arab commander with the SDF who was killed in August while fighting against IS in central Raqqa.
The loss of Raqqa would hand another major blow to IS, which has lost most of the territory it once held in Syria and Iraq.
Iraqi forces captured the northern Iraqi city of Mosul, the largest ever held by the extremist group, in July, and Syrian government forces retook the eastern Syrian city of Mayadeen, near the border with Iraq, yesterday.
IS still holds parts of Syria's Deir el-Zour province and Iraq's Anbar province, as well as small, scattered pockets elsewhere.
Yesterday, the US-led coalition and local officials said Syrian IS fighters and civilians would be allowed to leave Raqqa, but not foreign fighters. The evacuation appeared aimed at sparing the lives of civilians being used as human shields. As of last week, around 4,000 civilians were believed to still be in the city.
The SDF said the initiative by local tribesmen and members of the Raqqa Civil Council "succeed in evacuating civilians who were still in the city and the surrender of 275 local mercenaries and their families." It added that the ongoing offensive aims to "end the presence of mercenaries of the terrorist organisation inside the city."
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, said among the fighters who remain in Raqqa is an official who planned attacks in France that killed and wounded dozens of people. Abdurrahman said the man is either a French or Belgian citizen of North African origin.
Two Kurdish officials, Nawaf Khalil and Nasser Haj Mansour, said the evacuation took place early today, adding that some gunmen remained in a pocket they still control in Raqqa. Khalil said the civilians who left Raqqa included families of fighters.
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