The militants said coalition airstrikes had weakened the Tabqa Dam, some 40 kilometers west of Raqqa, and that the water level behind the dam was rising.
The extremists captured the city from Syrian rebels in 2014 and it now serves as the capital of the group's self-styled Islamic caliphate.
Civilians began fleeing midday, according to the activist-run Raqqa is Being Slaughtered Silently.
The Britain-based Syrian Observatory for Human Rights, an opposition-run monitoring group, today reported that the IS-held dam was out of service for unknown reasons.
Also Read
The reports from Raqqa came as a leading Syrian opposition group called on the US-led coalition to stop targeting residential areas in and around the city.
The Syrian National Coalition said in a statement that it was "increasingly concerned" about civilian casualties in the campaign against the extremist group.
The exiled opposition coalition is taking part in UN-mediated talks in Geneva. The SNC said it believed coalition forces were behind an airstrike that killed at least 30 civilians sheltering in a school in the countryside outside Raqqa on March 21.
The Britain-based Syrian Observatory for Human Rights said coalition airstrikes have killed 89 civilians in the Raqqa province in the past week, including 35 in the Badya school, in the village of Mansoura.
Disclaimer: No Business Standard Journalist was involved in creation of this content