And the Council's Social Portfolio Leader, Councillor Ngaire Best, says Mr Dunne's "insistence on pushing fiction rather than facts" is irresponsible.
"Mr Dunne appears to be ill-informed - and despite the fact that we have offered to brief him on our emergency-management arrangements, he has so far chosen not to take up the offer.
"I would hope that, in the event of a major emergency in Wellington, Mr Dunne would help the response by working collaboratively with us rather than spreading rumours not based on fact."
Mr Mendonca says Wellington City Council and the region's other councils and emergency services are well-prepared to deal with a big earthquake or other major civil emergency.
Mr Dunne's claim that the Council's Emergency Management Office is presently unstaffed is untrue. "What is true is that the office has been through a restructure - and that we are now in the process of appointing the new emergency preparedness manager - but the office still has up to five experienced staff keeping it up and running and prepared."
Mr Mendonca says it is important for Wellingtonians to know that, in the event of a big emergency, hundreds of City Council staff will work with emergency services, the Defence Force, the Ministry of Civil Defence and Emergency Management, volunteer groups, government and social agencies, and a host of other organisations to respond.
"The city's response to a major civil emergency does not rest on a few staff in our emergency management office.
"While the office plays an important role in the Council's interface with other emergency services and various community elements, its staff do not manage the emergency. This small team is part of a massively larger team of Council managers, hundreds of Council employees and contracted personnel who train regularly on how to respond to an emergency and how to work from the emergency management office in Thorndon.
"We're more than happy to sit down with Mr Dunne to give him a briefing about what's really going on.
"The City Council is proud of the progress made in recent years in the area of civil defence and emergency management. We have established a well-resourced emergency management office operating from a purpose-built facility and with access to significant resources that is the envy of many local authorities.
"We are however not content with our progress to date and want to aim even higher. We are not yet satisfied with the current level of community emergency awareness. We want to achieve 100% preparedness by Wellingtonians.
"We are also not satisfied with the current state of our volunteer networks. We have hundreds of well-trained and motivated volunteers around the city - but we need more.
"We want all our civil defence centres to be fully resourced with trained members. We believe that our coordination with other emergency services and regional authorities can be even better."
In terms of the issue over staffing at the emergency management office, three out of five permanent staff have resigned from their roles since September 2008 and have not been replaced at this stage. This is in order to allow senior Council managers to review the city's emergency management structures. However access to contracted staff and to the Council's resources means that the services delivered by the emergency management office are not compromised.
Once the new emergency preparedness manager has been appointed, the Council will make decisions on the future makeup of the office and its relationship, in terms of resources, with the rest of the City Council and with the Wellington Regional Civil Defence Emergency Management Group - which comprises CDEM representatives from Greater Wellington Regional Council and the other local authorities in the area.
Cr Best adds that it is also essential for Wellingtonians to remember that they and their families have to be personally prepared for an emergency. "This is a good time to remind people that they should store water and food and other emergency supplies at home - and that they should have a family preparedness plan."