Thousands of demonstrators called Sudanese President Omar al-Bashir a "killer" on Saturday, the sixth day of protests sparked by fuel price hikes in a nation already burdened by economic pain and war.
They said the "martyr" Salah Mudathir, 28, was shot dead during a protest the day before.
Police did not release names but said four civilians were gunned down by unknown shooters during demonstrations after Friday prayers in the capital Khartoum.
"Bashir, you are a killer," a witness said about 2,000 marchers -- men, women and youths -- shouted after Mudathir's burial.
"Freedom! Freedom!" he said they shouted, calling for the end of Bashir's regime, which calls itself Islamist.
The latest demonstration occurred after thousands of mourners walked through the streets of the wealthy Mansheeya neighbourhood escorting an ambulance carrying Mudathir's body, the witness said.
Mudathir, a pharmacologist, belonged to a family that is prominent in business and politics.
"He was killed by a bullet to the heart this evening" while he demonstrated, a cousin told AFP on Friday night, as women wept at the family's large home.
Police said Friday's protests in the capital had been mostly peaceful following weekly Muslim prayers but that some protesters blocked roads and created "disturbance."
"Police ended the demonstrations using tear gas in a limited way," a statement said.
But "unknown shooters fired on demonstrations in Khartoum Bahri, Khartoum and Omdurman" during the protests, added the statement, carried by the official SUNA news agency.
"As a result of that, four civilians were killed."
It is the first time police have confirmed that people have been shot during the protests, which are the biggest challenge to Bashir's rule.
Demonstrations began Monday after the government scrapped fuel subsidies, leading to soaring prices.
Police previously said 29 people had died but gave no details.
International rights groups say 50 were killed after being shot in the head or chest on Tuesday and Wednesday.
The powerful National Security and Intelligence Service, a bulwark of the regime which operates separately from police, has also been involved in the protest crackdown.
It was key to suppressing smaller-scale nationwide protests sparked by high food and fuel prices in June and July last year.
But there was no mass loss of life last year when authorities tear-gassed and rounded up demonstrators.
On Friday, the United States described this week's crackdown as "brutal" and said excessive force had been used.
The European Union also expressed concern about the deaths, calling on Khartoum to "respect the Sudanese people's right to freedom of expression, freedom of the media and freedom of assembly."
A spokeswoman for the UN High Commissioner for Human Rights in Geneva urged security forces to exercise "utmost restraint."
The protests began Monday in Wad Madani in Gezira state south of Khartoum, the scene of the first death, and later spread to Nyala, the capital of South Darfur state, and Khartoum itself.
"The people want the fall of the regime," protesters, many of them students, have chanted in Khartoum, echoing the refrain of Arab Spring protests that toppled several regional governments in 2011.