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The move would be considered at the next full council meeting, on May 19, after a plea from Emeritus Prof Sir Alan Mark on behalf of appeal organisers at this week's Dunedin City Council public forum.
The appeal urged the New Zealand Parliament to undertake an objective national assessment of the risks posed by climate change, economic instability and other potential threats to New Zealand's wellbeing.
It has already attracted about 6000 signatures and was presented to Labour, Green and New Zealand First MPs on the steps of Parliament on Saturday, although members of the Government failed to show.
Prof Mark told Monday's forum he hoped the council, or at least individual councillors and council staff, would add their names to the appeal.
That was because the urgency of the Government's response was likely to depend on how many people signed the appeal.
The Government would act only if public disquiet could not be ignored, he said.
The appeal tabled in Parliament was launched days after the release of the latest Intergovernmental Panel on Climate Change report.
Prof Mark told this week's meeting New Zealand had an important role to play in addressing climate change and other challenges, beginning by assessing the risks of a ''business as usual'' approach and identifying options.
He expected the appeal would be referred to a select committee, but progress from there would depend on the public's response.
''We would very much welcome the support of Dunedin City Council and staff,'' he said.
Mayor Dave Cull said council staff would prepare a report on Prof Mark's request, which would be considered at the council's May 19 meeting.