A total of 32 people have been arrested in connection with the incident which followed a peaceful Kill the Bill protest in the city.
The riot saw around 500 people march on Bridewell police station, set fire to police vehicles and attack the station.
Avon and Somerset Police said the latest people to be arrested were two men aged 23 and 36 and a 25-year-old woman.
A spokesman said: “With the new images added to the gallery there are currently 23 people we want the public’s help to identify.”
Anyone with information is asked to call 101, giving the letter of the person on the gallery, or through the force’s online form.
The independent charity Crimestoppers can also be contacted anonymously.
On Saturday, Ryan Roberts, 25, was remanded in custody after appearing at Bristol Magistrates’ Court charged with six offences relating to the riot.
He is accused of attempted arson with intent to endanger life by allegedly attempting to set fire to a police van, two charges of criminal damage, violent disorder and two charges of assaulting a police officer.
Roberts, of Easton, Bristol, will next appear at Bristol Crown Court on May 5.
Since the demonstration on March 21, there have been four other protests in Bristol against the Government’s proposed Police, Crime, Sentencing and Courts Bill.
Protests on March 23 and 26 ended in clashes between police and protesters. A demonstration on March 30 passed off peacefully.
Three people were charged with failing to comply with a dispersal order put in place following a protest on Saturday night.
Rebecca Buckley, 26, of Wilson Street, Bristol, and Thomas William Rix, 37, of Kingsdown Parade, Bristol, were released on unconditional bail and will appear at Bristol Magistrates’ Court on later dates.
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A 17-year-old boy will appear before Bristol Youth Court on April 28, a 17-year-old girl has been referred to the Youth Panel for a decision, and a 16-year-old boy has been released under investigation.
Two men aged 26 and 25 were given conditional cautions, Avon and Somerset Police said.
The proposed Police, Crime, Sentencing and Courts Bill would give police in England and Wales more power to impose conditions on non-violent protests, including those deemed too noisy or a nuisance, with those convicted liable to fines or prison terms.
