The Syrian Observatory for Human Rights said 21 children were among at least 59 civilians killed since Monday in the air strikes aimed at dislodging the jihadists from Raqa.
"The worst place probably today in Syria is the part of Raqa that is still held by the so-called Islamic state," the UN's humanitarian pointman for Syria, Jan Egeland, told reporters in Geneva.
The UN estimates there are up to 25,000 civilians trapped inside Raqa, the jihadist group's erstwhile de facto Syrian capital.
"We are therefore urging the coalition, the SDF whom we can deal with to allow as much as they can people to escape", the UN official added.
The SDF, a Kurdish-Arab alliance backed by the multinational coalition, was on Thursday battling the jihadists in Raqa's Old City, of which it now controls 70 per cent, according to the Britain-based Observatory.
The SDF 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.
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.
Humanitarian workers believe "the situation couldn't be worse for these women, children (and) civilians who are now in this crossfire," Egeland told reporters.
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