"An illegal gathering was held in Omdurman and police dispersed it with tear gas," police spokesman Hashim Abdelrahim said.
"Police later received reports that three protesters had died and several [had been] injured. We are now investigating," he added.
A doctor in the city told reporters that he had treated several people for gunshot wounds.
Omdurman is Sudan's second-largest city. Just across the Nile in the capital, Khartoum, a rally was being held in support of President Bashir. Crowds of people carrying pro-Bashir banners were reportedly brought to the city by bus, and Bashir himself addressed the crowd jubilantly.
'Revolution is the people's choice'Sudan has been gripped by increasingly dangerous protests for weeks, initially over the government's decision to triple the price of bread during dire food shortages and soaring inflation. Demonstrators are also calling on Bashir to step down immediately.
"Revolution is the people's choice," chanted the crowd as they blocked a key road in Omdurman on Thursday.
Bashir has maintained a tight grip on the country since he came to power in a coup in 1989. He has been accused of genocide and other crimes against humanity in Sudan's western Darfur region.
He was due to finally step down in an election in 2020, but the government has recently indicated that it will extend his current term.
The authorities have confirmed that 22 people have been killed in the unrest of recent weeks, but the NGO Human Rights Watch believes the death toll is closer to 40.
es/msh (AFP, AP, Reuters)