But despite the email, Briggs told the Herald there was no directive for staff to monitor elected members' social media pages.
"I have a high degree of trust and respect for elected members and assume they act in the best interest of the community and council at all times. Given this I don't see the need to monitor."
The post was more likely picked up by an electronic scan which the communications unit deemed important enough to forward to him, Briggs said. Any communication sent to him would be around managing and maintaining council's reputation and associated risk, he said.
"I hold a view that elected members are free to engage as they like as long as it doesn't breach the code of conduct."
However, in regards to the specific email. Briggs distanced himself saying: "I can't recall if I even read the email in question."
But O'Leary thought having a member of the communications department checking councillors' social media was "blurring the lines and not appropriate".
"The management is meant to be apolitical. I am allowed to speak to my constituents and I have always used my social media that way - to put out information, to express opinion.
"If the CEO wanted to see something on my Facebook he should just have a look for himself ... I think it unnecessarily involves a member of the staff and puts them in a difficult position."
Susan Hornsby-Geluk, a partner for Dundas Street Employment Lawyers, said the council's chief executive and his staff were responsible for running the operation and had no control over the elected members who were a self-governing body.
"The communication unit of council [is] obviously concerned about issues affecting the operation of the council, but seeking to restrict what elected members say would appear to go beyond that."
Councillor Dave Macpherson did not have a problem with elected members' posts coming up in broad searches, but said the fact it was forwarded to the CEO was "unnecessary" and left "a bad taste".
"No one in the staff should be officially monitoring anything that any elected members said - I've always felt that," he said.
"I don't think it's something staff should be spending their time on ... They shouldn't be doing it. They shouldn't feel the need to do it."
However, Mayor Andrew King disagreed and thought it was appropriate for council staff to be monitoring public Facebook pages to ensure statements being made were accurate.
"Elected members are allowed to have their personal views," he said, but if they were espousing views which were not based on facts, "then I would imagine [council] do have to know".
"It's in council's management interest to keep an eye on what is going on if it is in the public space of what is being said."
While councillor Geoff Taylor did not realise staff may be tracking their Facebook pages, he was "pretty relaxed about it".
"Everything we put out there is of interest to the organisation. It is pretty naive to think that you can put things on Facebook and other people in the organisation aren't interested. Get real, is my view.
"I don't see it as a great productive use of time by comms staff, but I don't really have a major issue with it."
