It comes after work demolishing the iconic building's badly damaged spire began this week, with a crane tentatively dismantling the masonry structure.
Representatives from the Anglican Church and the Historic Places Trust have been monitoring the work, which is expected to take a week.
Historic Places Trust board chairwoman Shonagh Kenderdine has called for the work to stop, and for the Cathedral to be supported and fenced off for public safety.
"The board recognises and respects the difficult decision made by the church,'' she said. "However, our engineering report by respected structural engineer, Win Clark, who is executive director of the Society of Earthquake Engineers, and other reports by seismic engineering experts indicate that the Cathedral can be retained in a greater form than what church leaders believe. It is a question of time and money, and time needs to be taken to find the necessary money.
"Christ Church Cathedral defines the city and province. It is a landmark that the whole community and visitors have an affinity with and is connected to, be it spiritual, physical, visual or emotional.''
The Anglican church announced in March the building would be deconstructed down to 2-3m, as the building is not safe and repair work is cost-prohibitive, however opponents of the move, including New Zealand and international seismic engineers, believe the building can be safely restored for around $30 million.
A online petition set up last week calling for the Cathedral to be saved has more than 1000 signatures.
