One person was killed and 21 injured at a demonstration in Ed Delenj on Monday and at least eight people were hurt in the violence in central Khartoum on Wednesday, students said.
Riot police surrounded Khartoum University, closing it down and threatened journalists who tried to enter.
Police officials declined to comment on the students' reports and ordered journalists to leave the scene.
The streets in the normally busy area were later deserted but covered in broken glass and rocks.
Secretary-General of Khartoum University Student's Union Tahamid Umar Gibril told Reuters the students union elections at Ed-Delenj in South Kordofan state were fixed so that the government's candidates won.
He said the march on Monday denouncing the election result turned violent after the police and army intervened.
"Students in Sudan show solidarity with each other," Gibril said. "We totally reject this kind of behaviour from this regime ... we reject the use of force ... to hinder our democratic rights," he said.
Ahmed Tayyib, an arts student, said police fired rubber bullets and unleashed clouds of tear gas on the students in Khartoum.
"They also beat them with sticks," he said, adding demonstrations at another central Khartoum university, an-Nilein, had also turned violent on Wednesday.
"The protests will continue until they change their ways," Tayyib said, referring to the government of President Omar Hassan al-Bashir which took power in a bloodless military coup in 1989.
Tayyib said security and police randomly arrested dozens of students.
Earlier on Wednesday a government-allied students union led a demonstration outside the French embassy in Khartoum to protests against a U.N. resolution referring alleged war crimes in Sudan's troubled western Darfur region to the International Criminal Court (ICC).
About 200 students gathered outside the embassy carrying banners saying "No to colonialism". They handed the deputy chief of mission a letter objecting to any Sudanese national being sent to a court outside the country.
France drafted the original version of the resolution, but Britain later took over its sponsorship.