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From December 3, a copy of My Vaccine Pass will be necessary to enter some events and venues, such as sporting events and close contact businesses.
The pass will not be necessary for basic needs services such as supermarkets.
A Ministry of Health spokesman said there would soon be an announcement on how people could obtain their vaccine pass through face-to-face channels.
"This could mean going into vaccinating pharmacies to obtain their pass," he said.
People would also be able to call up and request their pass to be posted. An emailed printable version would be available.
The ministry call centre was dealing with "unprecedented demand" from people looking to get their vaccine passes but the issues were being worked through, he said.
The ministry advised those who were able to go online to the My Covid Record website to request their pass.
Grey Power Otago president Jo Millar said it was aware of struggles among elderly people to get the pass.
Phone lines for the Ministry of Health were often jammed and many elderly people did not have the ID required to get the pass, such as driver’s licences or passports.
The upcoming improvements would make getting a pass easier for elderly people, she said.