"We have received the bodies of 21 people" since the protests began on Monday, a hospital source in Khartoum told AFP, adding that all were "civilians".
Another eight people were killed in other regions, witnesses and families said.
Activists have called for fresh protests today in Khartoum, where anti-riot forces have been deployed since early morning at the major road intersections, AFP said.
Riots broke out in several districts of the capital yesterday, some took place near the city centre, and the public transport ground to a halt, AFP reported.
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The US embassy called on its citizens to avoid flash point areas, saying it had received "regrettable" reports of casualties and warning Americans of the danger of further protests.
The Internet also remained cut today, users said, but it was still not known if the reason was a technical failure or a deliberate move by authorities.
The education authorities announced the closure of schools until September 30.
These protests are the largest Sudan has faced since President Omar al-Bashir seized power in 1989.