The Syrian Observatory for Human Rights said 21 children were among at least 59 civilians killed in the air strikes since Monday, after more corpses were dug out from under piles of rubble.
With air support from the multinational coalition, a Kurdish-Arab alliance on Thursday battled the jihadists in Raqa's Old City, of which it now controls 70 percent, the Britain-based group said.
The Syrian Democratic Forces also fought IS in the western district of Al-Dariya and the northwestern neighbourhood of Al-Barid, as well as on the outskirts of the central district of Al-Murur, it said.
But it has recognised 624 such deaths in its air strikes since 2014, a figure which many rights groups say is vastly underestimated.
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According to the United Nations, 25,000 civilians are trapped inside Raqa, the jihadist group's erstwhile de facto Syrian capital.
The SDF launched an operation to capture Raqa province from IS last year, and in June the alliance broke into Raqa city for the first time.
It now holds more than half of the city, but the fighting has proved fierce and civilians have been killed both in the crossfire and while trying to flee.