Both the council communications team and Mayor Nobby Clark refused to comment on the reasons for it.
The council held public-excluded extraordinary meetings on March 7 and March 18.
The minutes of the meetings stated the reason was "to discuss the requisition and letter received by all councillors" and "discuss letter received", respectively.
For the first meeting Mr Clark issued an apology as he was away "on council business". For the second meeting it was noted he had advised deputy mayor Tom Campbell he had an interest and therefore Cr Campbell would chair the meeting.
Both meetings were attended by the elected members, council’s independent risk and assurance chairman Ross Jackson and lawyer Mary-Jane Thomas.
In the meantime, a council spokeswoman confirmed yesterday chief executive Michael Day had been on leave since Tuesday and council community engagement and corporate services manager Trudie Hurst had been appointed acting chief executive.
"As with any time he is on leave, he appoints a member of the ELT [executive leadership team] to act in his role."
She did not respond to questions about what kind of leave he was taking, how long he would be on leave or if his absence was related to the closed-door meetings.
"The meetings were held in public excluded and we are not able to comment further on the nature of the meetings for the reasons set out in the agenda, which are to maintain legal privilege and to protect the privacy of natural persons."
Since the beginning of the year, Mr Clark had been campaigning to keep a rates increase to 3.9% as opposed to the suggested 9.47%.
In an interview in February, he told the Otago Daily Times he had been battling executive staff to get a breakdown of the council’s expenditure on contractors and consultants since he got into council and he had reached the point of filing an LGOIMA request to get this information.
"As a mayor, this was the first time I ever did that because I just can’t be fobbed off any more."
He also told The Southland Tribune his relationship with staff was a bit "frosty".
