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The incident, on Monday morning, was confirmed by Mr Cull and Cr Vandervis yesterday.
Cr Vandervis defended his actions, saying he acted in the public interest, but Mr Cull labelled his behaviour "highly unusual" and "unacceptable".
The office invasion was prompted by Monday morning's meeting of a council liaison group, established in March to act as an intermediary between councillors and the council's council-controlled organisations (CCOs).
The meeting, held in the Civic Centre building, was chaired by Mr Cull and attended by deputy mayor Chris Staynes and Crs Syd Brown and Richard Thomson.
Cr Vandervis - who was among councillors excluded from the meetings - told the ODT he decided to "simply turn up", after questions sent to Mr Cull about the group's activities were ignored.
Cr Vandervis said he walked in, took a seat and began unpacking his papers and laptop, and repeatedly refused to leave when challenged by Mr Cull.
Eventually, Mr Cull adjourned the meeting to his mayoral office. Cr Vandervis said he followed the group in and again took a seat.
He ignored more requests to leave, prompting Mr Cull to call security guards, but not even talk of a trespass order and a threat to call police could budge Cr Vandervis.
Cr Vandervis said two "rather spindly-looking" guards arrived and threatened to remove him, but changed their minds and said they would call the police.
Cr Vandervis said he began dialling the police on his cellphone, claiming the group's meeting was illegal because other councillors were excluded.
Instead, he eventually agreed to leave, followed by the security guards, after Mr Cull offered to meet him for an "amicable" and "productive" meeting about his concerns later in the day, Cr Vandervis said.
Monday's protest came after Crs Vandervis, Fliss Butcher and Teresa Stevenson criticised the CCO liaison group's creation in March.
The group was not to have decision-making powers, but aimed to provide a conduit between councillors and the CCOs when, for example, discussing commercially sensitive matters at short notice.
Mr Cull had ruled out allowing non-members to attend as spectators, but Cr Vandervis said yesterday his advice from a lawyer and from council staff was the exclusion of most councillors was unprecedented and illegal.
He claimed the group was making high-level decisions without oversight from excluded councillors; that his questions about the financial performance and directorship of the CCOs had been ignored; and no reports from the group had been received by the other councillors.
Mr Cull denied the group was illegal, saying most councillors - backed by staff advice - had voted to create the group and agreed to the exclusions.
The restricted membership allowed "full and frank" discussion with staff from the CCOs and parent company Dunedin City Holdings Ltd, while resolving "a few issues", which he would not detail.
"Basically, this is a matter of Cr Vandervis not accepting a council decision."
Cr Vandervis said he was satisfied by an assurance from Mr Cull more information would be provided and the group's meetings would cease next month.
"Obviously, they've had some major goose to cook and they've done it, or they're near to doing it, but I wouldn't know."
Mr Cull said the intention was to establish a new reporting mechanism for CCOs, as part of a governance review already under way. That would mean the CCO liaison group was no longer needed, he said.