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Covid-19 Response Minister Chris Hipkins has so far been reluctant to set a concrete target, saying last week: "We've never set a fixed target".
"We want to vaccinate as many people as possible."
But this morning, National said this was not good enough and a specific target was needed.
"New Zealand is one of only a few countries in the OECD that doesn't have a target for how many adults should be vaccinated. The others are Colombia and Mexico."
The UK, for example, has a target of having all 32 million adults in the country vaccinated by April 15 – so far, just under 30 million people have received the jab.
And Australia's Government has set an October deadline to vaccinate its population.
"The best [our] Government can say is that it wants all New Zealanders to be offered a vaccine by the end of the year," Bishop said.
"We should be setting an ambitious target and going for it. A target will make sure the health system is focused, and means vaccination progress can be meaningfully tracked."
He pointed out that the Government has targets when it comes to measles and flu vaccines.
Not having one for Covid-19, he said, suggests the Government "doesn't want to be held to account on this".
Speaking to reporters last week, Hipkins said the Government's target was to get as many people vaccinated as possible.
"We know towards the middle of the year, as we ramp up and make it publicly available, there will be a lot of demand."
At that time, Hipkins said, there would be more than 20,000 vaccines administered a day.
But, as New Zealand has to wait for the bulk of the Pfizer vaccines to arrive, the vaccination campaign has started out small – as had been signalled by the Government.
As of last Wednesday, there have been at least 41,500 vaccines administered.
That number will no doubt be higher today but, unlike other countries that provided daily vaccination numbers, New Zealand's information comes out just once a week.
This is something Bishop has also taken issue with.
He said New Zealanders should be getting near-daily announcements, published by the Ministry of Health, so everyone can see how our vaccine rollout is going.
"This isn't rocket science – it already happens with testing and tracing."
New Zealand is currently on to group two of the vaccination rollout.
That is, 480,000 frontline workers and people living in high-risk settings.
From May, New Zealand's more high-risk people and those over 65 with underlying health conditions will get the jab and the general rollout will begin in July.