"The Syrian Democratic Forces and American special forces began a mopping up operation in Raqa," the Syrian Observatory for Human Rights said.
The Britain-based monitor said jihadists were still hiding in underground shelters in a part of the city centre, where a football stadium and former government buildings are located.
But the operation was being slowed down by large numbers of mines planted by the extremists, it said.
The Syrian Democratic Forces, an alliance of Kurdish and Arab fighters backed by the United States, have been battling IS in Raqa since June after encircling them for months.
On Wednesday the SDF said they were in the "final stages" of capturing the northern city from the jihadists.
"We consider this the final stages of the Wrath of the Euphrates campaign, which is nearing its end," a statement said.
The SDF said it had mounted a "surprise attack" on IS in the north of Raqa, where the jihadists have been surrounded for three months.
The US-led coalition backing the SDF with air strikes, equipment and advisers said it had been bombing IS near Raqa for days.
The jihadists seized Raqa in early 2014, transforming the northern city into a key hub in the "caliphate" they declared after taking control of large parts of Syria and Iraq.
Raqa quickly became synonomous with the group's most gruesome atrocities, including public beheadings, and IS is thought to have used the city to plan attacks abroad.
Tens of thousands of civilians have fled the fighting in recent months but up to 15,000 are still trapped inside, according to the UN'S Office for the Coordination of Humanitarian Affairs (OCHA).
"We now estimate that up to 15,000 civilians remain trapped in Raqa city, although exact figures remain difficult to verify due to the situation on the ground," OCHA's Linda Tom told AFP.
According to her, the civilians, many of them women and children, "are facing incredibly difficult conditions", including food, water and medical shortages.
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