Thousands marched in the capital Khartoum and other cities on Saturday, demanding the reinstatement of ousted Prime Minister Abdullah Hamdok.
The interior ministry denied that live rounds had been fired. Activists say around 100 people were injured.
Coup leader Gen Abdel Fattah Burhan dissolved civilian rule this week.
The general, who also called a state of emergency, said his actions were justified to avoid “civil war” and stop political infighting. The military takeover has drawn widespread international condemnation.
Demonstrators in Khartoum were seen marching with Sudanese flags and chanting, “No to military rule!”