Civilian leaders say this would amount to a coup and say the military aims to install a government it can control.
Thursday's protest took place on the anniversary of the 1964 October Revolution and was preceded by days of smaller neighbourhood protests.
Reuters journalists estimated the number of participants to be in the hundreds of thousands, making it the biggest demonstration of the transition.
Plumes of smoke could be seen as protesters burned tires and waved Sudanese flags.
Many chants were critical of head of the ruling Sovereign Council, General Abdel Fattah Al-Burhan, accusing him of being loyal to Bashir. Some demanded he hand over leadership to civilians and others demanded his removal.
"The government is ours, and our government is civilian," one chant said.
Several government ministers were seen marching in different parts of Khartoum.
"October 21 is a lesson for any tyrants, loyalists, or opportunists deluded into thinking they can turn back the hands of time," wrote Sovereign Council member Siddig Tawer, one of several civilian officials who endorsed the protests.
Neighbourhood resistance committees said in a statement they were protesting the entire power-sharing agreement and demanded sole civilian rule.
Many businesses in central Khartoum were closed in anticipation of the protest and there was an extensive police presence.
The military says it is committed to the transition to democracy and elections at the end of 2023.
Prime Minister Abdalla Hamdok, who leads the cabinet under a military-civilian power-sharing agreement, remains popular despite an economic crisis. He has said he is speaking to all sides in the crisis in order to find a solution.
Military-allied groups led by former rebel leaders and current government officials Minni Minnawi and Jibril Ibrahim have held a sit-in in front of the Presidential Palace since Saturday.
Protest routes were planned in different areas away from the downtown area to avoid confrontation with the pro-military sit-in.
"We encourage demonstrators to be peaceful and remind them of the strong U.S. support for Sudan's democratic transition," the U.S. Embassy said in a tweet.
(Additional reporting and writing by Nafisa Eltahir; Editing by Angus MacSwan) ((Nafisa.Eltahir@thomsonreuters.com;))