Heavy gunfire was heard late into the evening, and the council said a military police officer had been killed and many protesters wounded. Local doctors said some were in serious condition.
The council accused armed groups unhappy with progress towards a political deal of opening fire at protest sites. Protesters said counter-revolutionaries linked to the former regime were inciting violence.
Earlier, paramilitary forces patrolled the streets, using tear gas and gunshots to disrupt protests blocking roads.
The Transitional Military Council (TMC) and the Declaration of Freedom and Change Forces opposition alliance were due to meet on Tuesday to discuss two key sticking points: the military-civilian balance of power in transitional bodies, and the length of the transition before elections.
Protesters are pushing for a civilian-led transition and have kept up demonstrations against the council since military officers on April 11 removed and arrested Bashir, who is now facing multiple criminal investigations.
On Monday morning, police and paramilitary Rapid Support Forces (RSF) dismantled barricades and dispersed about 100 protesters who had blocked a road leading from Khartoum North to al-Mek Nimir Bridge and the center of the capital.
For a second day demonstrators blocked Nile Street, a major avenue running south of the Blue Nile, placing burning branches and stones across the road, as well as several other streets north and south of the river.
Later, RSF men used gunfire to disperse protesters next to Blue Nile bridge and thick clouds of tear gas were fired near Jumhuriya Street south of the river, where the RSF were seen beating a rickshaw driver as they patrolled in vehicles armed with sticks and guns, witnesses said.
SIT-IN
Protesters demanding a swift handover of power to civilians have been camped at a sit-in outside the Defense Ministry compound in central Khartoum since April 6, as the military has negotiated with the opposition alliance over the transition.
Talks resumed on Monday, and both sides said they had produced agreement on the duties and authorities of sovereign, executive and legislative bodies.
"We discussed the structure of the transitional authority and agreed on it completely, and we also agreed on the system of governance in the transitional period," said TMC spokesman Lieutenant General Shams El Din Kabbashi.
"We will continue tomorrow with talks on the ratio of participation on the sovereign level ... and the length of the transitional period," he said. "God willing, we will agree on these two points."
The Sudanese Professionals' Association, which leads the opposition alliance, has accused the TMC of expanding its powers as talks over the transition have stalled, threatening a campaign of civil disobedience to up pressure on the military.
"The situation now on public roads, bridges and in neighborhoods expresses the state of popular discontent with the procrastination and the consumption of time by the military council," the SPA said on Monday.
The TMC has said it is not seeking power and is open to further dialog. General Mohamed Hamdan Dagalo, head of the RSF and deputy head of the TMC, told a military meeting on Monday that the armed forces and RSF were working to protect "security and stability" in Sudan.
Also on Monday, Sudan's public prosecution said it had charged Bashir and others with incitement and involvement in the killing of protesters.
Earlier this month, the public prosecutor ordered Bashir to be interrogated on charges of money laundering and financing terrorism. There has been no comment from Bashir, who is in prison in Khartoum.