In messages broadcast by the Sudanese state media, the regime threatened "stern measures" against the protests, which first targeted the austerity moves but have expanded to include calls for the ouster of longtime President Omar al-Bashir.
Several hundred students gathered at Khartoum University, where the demonstrations started eight days ago, said Kamal Omar of the Popular Congress Party. He said pro-government "militias" attacked them. Other opposition figures said police fired tear gas to break up the rally and arrested dozens of students.
The official SUNA news agency reported late Saturday that authorities instructed police to "deal sternly with saboteurs."
The regime is determined that "subversive incidents" would not deter it from implementing recent economic decisions, the news agency said.
Protesters reject a government austerity plan that slashed subsidies and doubled the price of fuel and food. They also appear to be inspired by Arab Spring uprisings that brought down regimes in neighboring Egypt and Libya and are demanding the downfall of al-Bashir's regime.
Demonstrations have been concentrated near Khartoum University on the banks of the Blue Nile river but have also spread to the city's far-flung outskirts and at least one provincial capital.
Representatives of Sudan's opposition parties say they have been meeting to come up with a unified stand on the protests. Police and security forces have arrested a number of party leaders in the past days, they say.