The group said four protesters died of gunshot wounds, and a fifth from choking on tear gas during clashes with security forces.
Tens of thousands took to the streets for mass anti-coup protests in cities and towns across the country.
Police denied using live wounds, saying they had only used “minimum force”.
State television reported that 39 police were “severely wounded” in the clashes.
The deadly violence comes days after a military-led ruling council was announced.
The military’s takeover on 25 October has drawn international condemnation.
Protesters have taken to the streets regularly since, demanding the military government step back and allow a peaceful transition to civilian rule.
Saturday’s protests went ahead in spite of a heavy security presence. Demonstrations were also held in solidarity abroad, including in Paris and Berlin.
AFP reports that protesters in the Sudanese capital of Khartoum were heard chanting: “No, no to military rule” and “down with the entire council”.
Reports of the five deaths were carried on the Facebook page of the Central Committee of Sudanese Doctors, which also reported a “large number of people” had been hurt.
In a tweet after the news broke, the US embassy in Khartoum condemned what it described as “excessive use of force” against citizens demonstrating “for freedom and democracy”.