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The National Party wants front-line workers, such as those working in managed isolation and quarantine facilities (MIQ), to get the vaccine as soon as possible.
Party leader Judith Collins wants the Government to consider emergency-use vaccine provisions for essential border workers "before it is too late".
"New Zealand has fallen behind the rest of the world with its vaccine programme and the Government needs to explain why," Collins said.
The Government has been approached for comment.
Yesterday, the Ministry of Health revealed there had been 31 new imported cases of Covid-19 since Thursday – all in managed isolation.
Of those, 19 were linked to the new, rapidly spreading strain of the virus which has taken hold in the UK.
"The number of cases reinforces the need for ongoing vigilance at the border, as Covid-19 continues to accelerate overseas," the Ministry of Health said.
But Collins said more than ongoing vigilance is needed to protect New Zealanders.
"It is critical we start vaccinating border workers and people working in managed isolation facilities as quickly as possible."
She pointed out that the Australian Government has recently brought forward its Covid-19 vaccine rollout. Health workers, border personnel and aged-care residents are at the front of that queue.
Collins wants New Zealand's Government to follow Australia's lead.
"Kiwis are rightly asking why Australia has plans to vaccinate four million people by the end of March while New Zealand won't start vaccinating the general public until at least July."
According to Prime Minister Jacinda Ardern, Covid-19 vaccines will be freely available to everyone in New Zealand midway through this year.
But border staff and rescue workers are at the front of the queue and will get the vaccine sooner than everyone else.
She said the mass vaccination programme would be New Zealand's largest immunisation roll-out in history.
"We are moving as fast as we can, but we also want to ensure the vaccine is safe for New Zealanders.
She said the Government had struck a deal with a number of pharmaceutical companies.
The agreements secure access to 7.6 million doses from AstraZeneca, enough for 3.8 million people, and 10.72 million doses from Novavax, enough for 5.36 million people.
Both vaccines require two doses to be administered