Both the army and RSF have struck densely packed areas in a war that broke out in April 2023 over the integration of the two forces.
The RSF in a statement denied targeting the market and instead accused the Sudanese army of launching attacks targeting civilians.
The conflict in Sudan has killed tens of thousands of people, driven millions from their homes and plunged half of the population into hunger.
Culture Minister Khalid al-Aleisir condemned the attack, saying that the casualties included many women and children.
He also said the attack, which he blamed on the RSF, caused "widespread destruction to private and public properties".
"This criminal act adds to the bloody record of this militia," he said in a statement.
"It constitutes a blatant violation of international humanitarian law."
We strongly condemn the treacherous terrorist attack launched today by the rebellious Rapid Support Forces militia on Sabreen Market in Omdurman, which resulted in numerous innocent civilian casualties, including children, women, and the elderly, as well as widespread destruction…— Khalid Ali خالد علي (الإعيسر) (@Aleisir) February 1, 2025
Sudan's Doctors Syndicate condemned the RSF's attack.
It said one shell hit metres away from al-Naw hospital, which received most of the market casualties.
It said most of the bodies taken to the hospital were of women and children, adding that the hospital has a significant shortage of medical teams, especially surgeons and nurses.
The conflict in Sudan started in 2023 when simmering tensions between the leaders of the military and the RSF exploded into open fighting in the capital Khartoum and other cities across the sprawling northeastern African country.
Saturday's attack was the latest tragedy in the country's brutal civil war.
Last week, about 70 people were killed in a RSF attack on the only functional hospital in the besieged city of El Fasher in the western region of Darfur.
The conflict has killed more than 28,000 people, has forced millions to flee their homes and has left some families eating grass in a desperate attempt to survive as famine sweeps parts of the country.
It has been marked by gross atrocities including ethnically motivated killing and rape, according the United Nations and rights groups.
The International Criminal Court said it was investigating alleged war crimes and crimes against humanity.
The US administration of former president Joe Biden accused the RSF and its proxies of committing genocide in the war.
In recent months the RSF has suffered multiple battlefield blows, giving the military the upper hand in the war.
It has lost control of many areas in Khartoum and the eastern and central provinces.
with AP
