People chanted "peaceful, peaceful" as they got out of a mosque in the town of Omdurman following weekly Friday prayer.
Protests also took place in some areas of northern Khartoum after the prayer, witnesses said, Presstv Reported.
People also marched in the streets of the eastern city of Atbara, where demonstrations first erupted last week.
Civil society groups said authorities detained nine opposition figures on Thursday evening ahead of a planned protest.
A committee of professional organizations involved in the demonstrations said in a statement that Siddiq Youssef, a senior leader of Sudan's Communist Party, as well as leaders from the pan-Arab Ba'ath and Nasserist parties were among the nine arrested people.
For more than a week, Sudan has been gripped by mass protests triggered by rising prices and shortages of food and fuel. The public display of anger later escalated into calls for President Omar al-Bashir to go.
The country is mired in economic woes, including an acute foreign currency shortage and soaring inflation, which is running at close to 70 percent.
Authorities have declared curfews and states of emergency in several states. Residents say police have used live ammunition in some cases to disperse the protesters.
Amnesty International said on Tuesday that Sudan's security forces had shot dead at least 37 protesters during the demonstrations. However, the information ministry said at least 19 people have died, including two military personnel.