Despite the bloody crackdown, both sides came to a power-sharing agreement last week that paves the way towards holding fresh elections in three years.
They were previously scheduled for Saturday evening.
The "Justice First" marches were called by the Sudanese Professionals' Association, which has been spearheading the protests since December.
On 3 June, crowds were violently dispersed by men in military fatigues in a pre-dawn raid on a protest site outside the army headquarters on 3 June, as demonstrators who had camped there for weeks demanding a civilian rule were shot and beaten. There were protests in other places, including the Red Sea city of Port Sudan and the eastern province of Kassala.
"Blood for blood, even if (we get) civilian rule!" protesters chanted.
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In Khartoum on Saturday, thousands protested on Sitteen Street, a major thoroughfare in the capital, a Reuters witness said.
Several hundred also demonstrated in Khartoum's Burri neighbourhood, a working-class district and the cradle of numerous protests.
Earlier, security forces had closed all roads leading to the presidential palace and deployed along the road leading to the airport.
Footage and photos posted by the SPA showed thousands of people demonstrating in the capital and its sister city of Omdurman.
Witnesses said many protesters were carrying banners that read: "Justice for Martyrs" while others held photographs of demonstrators killed in the raid.
Bashir was ousted by the army on April 11, five days after the protesters had first massed outside army headquarters.
The military council insists it did not order the raid, which according to the protest movement killed more than 100 and wounded hundreds in just one day.
Sudan's ruling transitional military has foiled a "coup attempt" aimed at "blocking the deal" with opposition representatives.
Intensive mediation of the African Union and Ethiopia led to a July 5 consensus on forming a "civilian and military" sovereign council to manage the country.
Sudan's Transitional Military Council (TMC) on Saturday reiterated importance of partnership with the opposition Freedom and Change Alliance to end the political crisis in the country.
"We are in a real partnership".