The statement by Sudan's National Human Rights Commission was the first acknowledgement by a state body that live ammunition has been used since protests erupted last month.
But the commission, whose members are appointed by President Omar al-Bashir, stopped short of saying who had fired the deadly rounds.
"We condemn using bullets against citizens," a statement said, in addition criticising the firing of tear gas at hospitals.
"We are also deeply sorry about the killing of citizens by bullets."
The commission said it was "calling upon the government to investigate this and bring the criminals to court".
Deadly protests have erupted across Sudan since December 19 when the government tripled the price of bread.
At least 22 people, including two security personnel, have been killed during the protests and hundreds wounded, officials say.
Rights groups have put the death toll much higher, with Human Rights Watch on Monday saying at least 40 people have been killed, including children and medical staff.
On Wednesday, a medic at the main hospital in Omdurman, the twin city of Khartoum, said that six protesters were treated for gunshot wounds after riot police broke up a rally.
A group of doctors from the hospital said separately that police had fired tear gas at the facility and there was also "shooting inside the hospital".
The state rights commission urged fact finding committees set up by Bashir to look into the overall violence and called for a report into the Omdurman incident.
"We are calling on all parties to protect hospitals, mosques and churches from any kind of violence or tear gas as these are protected areas," the commission said.
The protests that first broke over the price rise have quickly turned into anti-government demonstrations, with angry crowds calling for an end to Bashir's three decades in power.