The man, in his 70s died in his Kingswell home on Tuesday evening.
The man was undergoing a post-mortem this afternoon.
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Until those results were available, director-general of health Ashley Bloomfield would not say if his death would be added to the national total of nine Covid-19 deaths.
When asked if the man had links to the Bluff cluster, Dr Bloomfield said: "Yes, it is linked to the Bluff wedding; not directly, but indirectly.''
The Buff wedding cluster was connected to three more Covid-19 cases yesterday; it has been connected to 92 cases overall, including the death of a man in Wellington.
No new cases of Covid-19 were reported in the southern region.