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Mr Cull responded to the email, which was sent to all councillors, the Saddle Hill community board and media, by sending to the same group an email denouncing Cr Vandervis' email as derogatory and destructive.
In the email Cr Vandervis also suggested Cr Weatherall was keen to defend the existence of community boards to protect his son Scott Weatherall's income for being a member of a board.
Board members are paid about $8000 a year.
After being asked to by Cr Weatherall, Cr Vandervis publicly withdrew his comment and apologised to Cr Weatherall.
Mr Cull said canvassing issues was fine, but when an elected member repeatedly and baselessly questioned the integrity of, and belittled, other elected representatives, as Cr Vandervis did, it lessened people's respect for the council.
Mr Cull said on friday "a number" of councillors had expressed concern to him by email about Cr Vandervis' email, but none of those emails was officially a code of conduct complaint.
He could make a complaint himself, but felt he had expressed his opinion clearly already. He could still receive a complaint about it, he said.
Cr Weatherall said he was going to take a few days to think on it, before deciding if he would make a complaint.
The council's standing orders include a code of conduct that requires members to conduct their dealings with each other in ways that avoid aggressive, offensive or abusive conduct.
It also says comments to media must observe the requirements of the code.
Cr Vandervis is the subject of several ongoing conduct complaints from September last year, made after he abused staff in emails and released confidential information about the Haka Peepshow public art project.
He also laid a complaint about Mr Cull about issues, including the mayor's handling of points of order during council meetings.
The complaints had been in mediation and were still unresolved, Mr Cull said, but the affected parties were all aware of what was happening and he expected it would "play itself out", although he was not sure how, or how long it would take.
Punishments for breaching the code range from apology to suspension from some posts of responsibility.
Council staff were instructed last year not to speak to Cr Vandervis directly after a series of what Mr Cull described as "abusive" emails, in which the councillor gave orders to some staff and told senior managers to "call the DCC dogs off" after parking wardens ticketed cars left in the central city after heavy snow.