"Dozens of police have begun to beat the students with batons in Jackson Square," one demonstrator called Mohamed Salah told Reuters. "Some have been arrested."
A Reuters witness said armed riot police fired teargas and surrounded students in at least two universities in the capital.
Hundreds of heavily armed police began to patrol all Khartoum's main streets on Sunday morning as young people started gathering. Government newspapers carried front pages ordering people not to go out onto the streets.
Groups have emerged on social networking sites and Sudanese websites, calling themselves "Youth for Change" and "The Spark", since the uprisings in nearby Tunisia and close ally Egypt this month. One Facebook group had attracted almost 15,000 members by Sunday morning.
Messages on Facebook suggested the organisers were hoping to echo neighbouring Egypt's uprising and overthrow the Khartoum government, which they blame for high prices and accuse of curbing freedoms.