The director of Omdurman hospital told the BBC his staff had seen 21 bodies.  Three others died at another hospital.
Earlier police fired tear gas at protesters. The unrest began on Monday when the government lifted fuel subsidies to raise revenue.
Sudan's economy has been in trouble since South Sudan ceded in 2011.
Osama Mortada of Omdurman hospital told the BBC's Arabic Service that 21 people sent to his hospital had died, and that about 80 were injured.
"All have gunshot wounds, some in the chest," he said.
Also on Wednesday, sources at Khartoum Bahari hospital told the BBC that the facility had received three bodies "shot by live bullets earlier today".
Groups of anti-government demonstrators set fire to a university building and several petrol stations in Khartoum.
They blocked a main road to the airport and burnt a number of cars, witnesses say.
Correspondents say the Sudanese government's latest austerity measures have almost doubled fuel prices and hit the poor hardest.
Sudan had experienced an oil-fuelled economic boom until South Sudan became independent, taking 75% of its oil reserves.
The government reduced some fuel subsidies in July 2012, prompting several weeks of protests and a security crackdown.
The demonstrations began south of Khartoum and have now spread to the capital and other cities.
Officials have condemned the protests as acts of sabotage, describing them as "premeditated", according to the Associated Press news agency.
The Sudan Media Centre quoted Al-Zubair Bashir Taha, the governor of Gezira, south of Khartoum, as saying that aside from police stations, riots there targeted power and gas stations, banks, shops and private property.
Politicians, including President Omar al-Bashir, have defended the austerity drive, saying the only alternative would be economic collapse, local media said.
In a statement released in Arabic, the US embassy in Khartoum called for calm.
"We call on all sides not to resort to force and to respect civil liberties and the right to peaceful assembly," the statement said.
The embassy said it had received "regrettable reports of serious injuries and attacks on property during demonstrations which turned violent".
At least 24 people have been killed in the Sudanese capital Khartoum in clashes sparked by cuts in fuel subsidies, medical sources say.