U.S.-backed Syrian opposition fighters have been trying to capture the city from the Islamic State of Iraq and Syria (ISIS) since June 6, and have been marching under the cover of airstrikes by the U.S.-led coalition.
The Kurdish-led Syrian Democratic Forces (SDF) now hold more than half of Raqqa, the de facto capital of ISIS.
The Britain-based Syrian Observatory for Human Rights said on Tuesday that airstrikes on Raqqa the day before killed 42 civilians including 19 children and 12 women.
The Observatory, which relies on a network of activists and medics on the ground in Syria and generally proves a reliable source of information on the war, says coalition strikes have left 170 civilians dead in the last week alone.
The activist-run group Raqqa is Being Slaughtered Silently said 32 people were killed in airstrikes on one neighborhood on Monday.
Syrian state media also said the airstrikes had killed dozens, and blamed the U.S.-led coalition.
In June, a top United Nations human rights official said the U.S.-led coalition fighting ISIS in Syria and neighboring Iraq had caused a "staggering loss of civilian life," citing specifically the airstrikes around Raqqa.
"We note in particular that the intensification of airstrikes, which have paved the ground for an SDF advance in Raqqa, has resulted not only in staggering loss of civilian life, but has also led to 160,000 civilians fleeing their homes and becoming internally displaced," said Paulo Pinheiro, chairman of U.N.'s Independent Commission of Inquiry on the Syrian war.
Pinheiro told the U.N.'s Human Rights Council Wednesday in Geneva that, "the imperative to fight terrorism must not, however, be undertaken at the expense of civilians who unwillingly find themselves living in areas where ISIL (ISIS) is present."
There has been a dramatic increase in reported civilian deaths resulting from U.S. and coalition airstrikes in both Syria and Iraq since the beginning of the year.
U.S. military officials insist there has been no change in the rules of engagement for American forces operating in those two countries against ISIS, and say higher civilian casualties were always expected as the militants are increasingly squeezed into shrinking territory.