Covid-19 Response Minister Chris Hipkins says the latest case of an infected MIQ worker poses a "low risk".

The adult relative of the infected MIQ cleaner has now tested negative for the virus. An earlier "weak positive" result was now considered a false positive.

The worker's genome test showed the case was related to a guest at the Grand Millennium hotel.

There remains one location of interest: the Mt Roskill Countdown supermarket which the cleaner visited for 15 minutes from 3pm on Saturday before testing positive.

Criteria for early vaccinations

The Government has confirmed Kiwis can apply to get the jab early if they are travelling overseas.

Hipkins said there were strict criteria for these for early vaccinations – and only would be granted "for people who need to travel outside of New Zealand on compassionate grounds or for reasons of national significance".

The compassionate grounds that would be considered for travel overseas include:

• those needing to provide critical care and protection for a dependant;
• those accessing critical medical care that is not available in New Zealand
• those visiting an immediate family member who is dying.

"This does not include reuniting with family, attending a funeral or memorial service, or attending a school or university," Hipkins said.

The "national significance" overseas travel grounds cover those representing New Zealand in an official capacity:

• at significant international events;
  • and in an official non-government capacity

The international travel rules would apply to people who were travelling "in our national interest", Hipkins said.

"It will not include private, or recreational travel."

New Zealand Cricket said earlier this month that it was hoping its leading players will be some of the first people in the country to receive Covid-19 vaccinations outside of border workers, their families and front-facing health workers.

The organisation confirmed it is in discussions with the Government ahead of a busy year of touring for the Black Caps, including competing in the inaugural World Test Championship final in June.

Hipkins said it was in the Government's interest to protect those heading overseas with the vaccine.

Applications will open on March 31.

There have been 41,500 vaccinations in New Zealand to date.

By next Tuesday, there will be 50 clinics around New Zealand.

Those clinics will administer the vaccines.

Last week, Hipkins revealed 27,000 people had received a vaccination and just "10 to 20" people had refused the jab.

He said this was a "good, solid start" and the Government was making "good progress".Last week, Hipkins revealed 27,000 people had received a vaccination and just "10 to 20" people had refused the jab.

He said this was a "good, solid start" and the Government was making "good progress".