They want Jacinda Ardern’s Government to re-evaluate all types of co-operation between New Zealand and Myanmar, including business, social and education.
They want it to condemn the use of lethal force against civilians and to continue to voice support for human rights, democracy and justice in the Southeast Asian nation.
"We would like to express our heartfelt gratitude for New Zealand’s fine example in standing firm against the coup d’etat," a Dunedin pro-democracy Myanmar community group wrote in an open letter to Ms Ardern.
"We sincerely hope that you and your government will join in our people’s efforts to restore a democratic government."
Protesters have poured into the streets in Myanmar since a military coup on February 1 deposed the civilian government.
Hundreds of people have been detained for participating in protests.
Several protesters have been killed during the protests and many others injured over the past two days, after police in Myanmar fired stun grenades, tear gas and live rounds at demonstrators, according to local media.
New Zealand does not recognise the legitimacy of the military-led government and has called on the military to release detained political leaders and restore civilian rule.
All high-level political and military contact has been suspended.
Dunedin has a significant link with Myanmar’s deposed civilian government.
Henry Van Thio, second vice-president since 2016, lived in Dunedin from 2011 to 2015 and worked at Silver Fern Farms’ Finegand freezing works while his wife Anna Sui studied towards a PhD at the University of Otago.
A Dunedin protester gave the Otago Daily Times a copy of a speech that would have been presented at the Octagon if the planned march there had gone ahead.
The military regime had become increasingly violent in its response to peaceful, unarmed protesters, activists and political leaders, the person said.
"We want the military regime to hear our opposition."