Eyewitnesses said live and rubber bullets were used on protesters in nightly protests in Bahri, across the river from the capital Khartoum.
The United States and United Nations have dialled up the pressure on Sudan's new military junta as confrontations between soldiers and anti-coup protesters took the death toll to at least 11.
After the 15-member UN Security Council called for the restoration of Sudan's civilian-led government – toppled on Monday – US President Joe Biden said his nation like others stood with the demonstrators on Thursday.
"Together, our message to Sudan's military authorities is overwhelming and clear: the Sudanese people must be allowed to protest peacefully and the civilian-led transitional government must be restored," he said in a statement.
"The events of recent days are a grave setback, but the United States will continue to stand with the people of Sudan and their non-violent struggle," said Biden, whose government has frozen aid.
The UN Security Council, along with other foreign powers, called for restraint, dialogue and freedom of detainees.
UN special representative to Sudan Volker Perthes has offered to facilitate dialogue between Burhan and ousted Prime Minister Abdalla Hamdok.
With thousands taking to the streets to oppose the takeover led by General Abdel Fattah al Burhan, witnesses said live and rubber bullets were used on protesters in Bahri, across the river from the capital Khartoum as nightly protests picked up.
A doctors committee, which tracks the violence, said a "martyr" died in those clashes while two others were wounded and in critical condition. Earlier, a 22-year-old man died of gunshot wounds, a medical source said.
That took the total of fatalities in four days to at least 11, medical sources said.
On Thursday night, Burhan said in a speech to groups who helped remove dictator Omar al Bashir in 2019 that consultations were underway to select a prime minister, according to a video aired by Al Jazeera TV.
He said that the army is negotiating with Hamdok of the now dissolved transitional council to form the new government.
"Until this night, we were sending him people and telling him ... complete the path with us, until this meeting with you, we were sending him people to negotiate with him and we are still having hope," Burhan said.
"We told him that we cleaned the stage for you ... he is free to form the government, we will not intervene in the government formation, anyone he will bring, we will not intervene at all".
Sudanese officials at some ministries and agencies of government have defied the new junta, refusing to step down or hand over duties.
They have declared a general strike, along with unions in sectors from healthcare to aviation, although officials say they will continue to supply flour, gas and emergency medical care.
The former premier, initially held at Burhan's residence, was allowed to return home under guard on Tuesday. A source close to him said he remains committed to a civilian democratic transition and the goals of the revolt that toppled Bashir.
A group of ministers from the toppled government attempted to visit Hamdok on Thursday but were turned away, said irrigation minister Yasir Abbas.
With authorities restricting internet and phone signals, protesters have been handing out fliers calling for a "march of millions" on Saturday under the same slogan – "Leave!" – from the protests that brought down Bashir.
The latest of several recent coups in Africa ended a shaky transitional set-up in Sudan intended to lead to elections in 2023. Power was shared between civilians and the military following the fall of Bashir, whom the army deposed after a popular uprising two years ago.