Gunfire was heard overnight in particular near a central police station in Bangui, they said, adding that several shops and homes were looted during the dusk-to-dawn curfew.
Medical sources said that in addition to the more than 20 dead, around 100 people were wounded in Saturday's violence sparked by the murder of a motorcycle-taxi driver in central Bangui's Muslim-majority PK-5 neighbourhood.
The area was the epicentre of unprecedented killings between Christians and Muslims in the city in late 2013 and early 2014.
The chronically unstable country descended into bloodshed after a 2013 coup ousted longtime leader Francois Bozize, and it remains prey to violence between Muslim Seleka rebels and Christian militias known as the "anti-balaka", or anti-machete.
Although unrest has abated considerably, armed groups still operate in some parts of the country.
Presidential and legislative elections are due to be held by the end of the year, but they have already been pushed back several times as the country continues to grapple with the crisis.