The PSNI is investigating 57 separate reports of potential offences relating to bonfires over the Twelfth period this year.
Police said the potential offences include theft and destruction of political material, flags, hate slogans and effigies.
Politicians condemned the burning of posters, placards and effigies on a number bonfires across Northern Ireland.
Twelfth commemorations in Northern Ireland mark the victory of Protestant King William of Orange over Catholic King James II at the Battle of the Boyne, north of Dublin, in 1690 – a triumph that secured a Protestant line of succession to the British Crown.
Assistant Chief Constable of Local Policing, Bobby Singleton, said officers have "already gathered and secured evidence of potential offending, appointed investigators, commenced enquiries for each of these incidents and engaged with the Public Prosecution Service (PPS)" over the reported incidents.
He added that the PPS would "ultimately have responsibility for decisions in relation to prosecution".
“The vast majority of people celebrate their culture peacefully and lawfully and do not want cultural celebrations to be undermined by anti-social behaviour, criminal activity or hate directed towards others," said ACC Singleton. “I’m appealing for anyone with any further information but specifically information on those who may have been responsible for the potential offences to provide it to the police to bring those responsible to justice," he added.
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