"Unknown shooters fired on demonstrations in Khartoum Bahri, Khartoum, and Omdurman" yesterday during protests, the police said in a 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 five days of protests by thousands, in the biggest challenge to the 24-year rule of President Omar al-Bashir.
Demonstrations began on Monday after the government scrapped fuel subsidies, leading to soaring prices.
International rights groups say 50 were killed after being shot in the head or chest on Tuesday and Wednesday.