Protests broke out on Sunday in Darfur after calls for rallies there by the Sudanese Professionals' Association, which has spearheaded the demonstrations.
Police fired tear gas at demonstrators who took to the streets of el-Fasher, the capital of North Darfur state and in Niyala, the capital of South Darfur state, witnesses said.
The demonstrations in Darfur were the first of their kind since unrest erupted last month over a government decision to triple the price of bread, Presstv reported.
The protests have since swiftly escalated into nationwide rallies widely seen as the biggest threat to Bashir's rule in his three decades in power.
Protesters who took to the streets in the capital's Bahari district chanting "peace, peace" and "revolution is the people's choice" were quickly confronted by riot police.
Protest organizers have called for near daily demonstrations across the country against Bashir this week, calling it a "Week of Uprising."
In Khartoum on Sunday, protesters were seen carrying the Sudanese flag as others held banners bearing the words "peace, justice, freedom," which has become a key slogan in the rallies.
Police arrested several protesters, witnesses said, as footage of the rally which could not be independently verified spread on social media networks.
Sudan has been gripped by mass protests triggered by rising prices and shortages of food and fuel since December 19. The public display of anger later escalated into calls for President Bashir to go.
Authorities say the protests have left 24 people dead, while Human Rights Watch has put the death toll at 40, including children and medical staff.
Rights groups say more than 1,000 people have been arrested since the protests began, including opposition leaders, activists and journalists as well as demonstrators.