Police have already arrested 104 people as part of the probe, with 75 of them charged and 10 reported to the Public Prosecution Service.
Now they have re-issued 24 still images taken from video footage of “people they want to speak to as part of their inquiries into riotous and disorderly behaviour in connection with recent serious public disorder in north and east Belfast on July 12”.
Detective Superintendent Sean Wright said the investigation has received strong support from the public so far and wants that to continue.
He said: “There are people out there who will know the identity of these 24 people who I am looking to speak to. I am confident that those people will come forward with that information.
“It is vital that we all send out a message to those involved in public disorder that such behaviour will not be tolerated. Those who break the law must face consequences for their actions. They will be dealt with appropriately and proportionately through the criminal justice system.”
And he also appealed directly to those featured in these images to contact his team directly.
He added: “I would ask anyone who believes one of the images is of them to contact us immediately in order to help us with our inquiries.”
Clashes developed when police enforced a ban on an Orange Order march from returning through the predominantly nationalist Ardoyne area of Belfast.
Chief Constable Matt Baggott described the trouble, which injured dozens of police officers, as “shameful and disgraceful”.
The Operation Titan team is investigating a broad range of offences including the attempted murder of police officers, blast bomb attacks on police, hi-jackings, rioting throughout the Greater Belfast area, breaches of Parades Commission determinations and unlawful protests.
The PSNI has urged anyone who may be able to identify any of the individuals to contact them on 028 90901775 from 9am to 10pm Monday to Friday, or a message can be left outside these hours. Information can also be passed on anonymously through Crimestoppers on 0800 555 111.