Graffiti has been on walls for five days but police say its not for them to remove
Police said they were working to ensure threatening graffiti in east Belfast relating to the Avoniel bonfire dispute could be removed at the "earliest opportunity".
However, a senior officer stressed it was not the job of the police to remove the offending material.
Belfast City Council abandoned an attempt to demolish a bonfire on the grounds of Avoniel Leisure Centre in east Belfast when hired private contractors pulled out of the job after menacing threats were daubed on walls close to the site, purporting to identify them.
Five days after it appeared some of the graffiti remained with the council saying safety concerns prevented its total removal.
On Saturday the PSNI Chief Constable blamed the UVF, saying it had to be faced down over intimidation.
Assistant Chief Constable Alan Todd said: “The Chief Constable is on record publicly stating that the intimidation of contractors and the impact this will have had on them and their families must not be tolerated. A thorough police investigation is now underway to identify those responsible and seek to bring them before the courts.
“The removal of graffiti is the responsibility of the property owner assisted by any other relevant agency. It is not a function for, or the responsibility of the police service.
“Officers are in ongoing liaison with the property owners and with Belfast City Council in an attempt to ensure the removal of the offending graffiti at the earliest opportunity.
“As a police service we have been clear in our position that we will support other agencies to carry out their statutory functions in the removal of this graffiti and we are ready to do so in order to address any community safety issues and to ensure that there is no breach of the peace.”
Police accused the east Belfast UVF of mobilising and orchestrating its members to resist the bonfire's removal over the past week.
He was asked about the delays in removing the threats during a press conference on Saturday.
Mr Byrne said the graffiti was "unacceptable".
"It's a form of bullying and threat," he said.
"In terms of the police responsibilities I am clear that we will support other agencies to carry out their statutory functions."
He said his officers had been in contact with the council on the issue.
It has emerged that police units were poised for deployment on two occasions during the week to escort contractors to the site - overnight on both Tuesday and Wednesday - but the plans were aborted at short notice because contractors pulled out on each occasion.
As part of the fallout from the episode, the council has asked police to investigate how closely guarded details around contractors came into the public domain.
On Saturday, Mr Byrne rejected any suggestion the names of the contractors were leaked from within the police, insisting there were "no facts" to support such a contention. It is understood the police investigation is centred on the suspicion that the leak emanated from within the council.
Council officials, its thought, were monitoring the situation in the area over the weekend to determine when it would be safe to return to complete the work.
A council spokeswoman added: "Threatening graffiti at a number of sites was removed by council staff last week.
"However, the health and safety of staff is a priority and employees cannot carry out their duties where there is any potential for threat or intimidation."