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The department store has decided not to renew its lease, due to expire in September.
Kmart will explore other sites for reopening an outlet in Dunedin.
A company spokeswoman said it was committed to being part of the city "well into the future".
No timeframe has been provided for a reopening.
The announcement of the Meridian premises closure followed weeks of speculation about Kmart’s plans.
It has been shut since late March, when New Zealand went into lockdown.
The company has cited concerns about earthquake strengthening needed at the mall, but it was also known to be looking into other possible sites.
Kmart’s move is another blow for the central city mall, which will lose another large tenant, H&J Smith, next January.
"We’ve had a great relationship with Meridian mall for the past 23 years and are sad to announce that we will not be reopening our doors in this centre," Kmart said in a statement last night.
The company decided it would not renew its lease unless the building had a seismic rating above 67% of the new building standard.
The mall has a rating below 34% but site manager Oyster Property Group has said this applied only during earthquakes and it would be years before any strengthening work was necessary.
Kmart said it was "in the process of exploring locations that meet our requirements and are committed to being part of the Dunedin community well into the future".
"We hope to retain as many team members as possible and will provide an update ... as soon as we can confirm a new location.”
Oyster retail asset manager Jennifer Andrews said the group had been advised of Kmart’s plans.
"We’ve had a great relationship with Kmart for many years and we are naturally disappointed to see them leave Meridian mall," she said.
"We will be talking with new retailers and look forward to welcoming a new tenant."
Ms Andrews said the group was working on design plans for the seismic upgrade.
The mall had a building warrant of fitness and Dunedin was categorised as a low seismic risk under the Building Act.