One of the new cases has been classified as historical and deemed not infectious, the ministry said.
Three previously reported cases have now recovered, meaning the total number of active cases in New Zealand is 85. They are all in isolation.
"No additional UK or South Africa variants have been identified in genome sequencing from the latest weekly sequencing run by ESR and reported to the Ministry," a spokesperson said.
"Due to a post-holiday season related lag, positive samples from Auckland were not included in this sequencing run and will be sequenced and reported on Wednesday."
The spokesperson also said that all travellers arriving into New Zealand - excluding Australia, Antarctica, and some Pacific nations - are now required to have day 0/1 tests and stay in their rooms until the result is known.
"This requirement will be progressively introduced over three days starting today."
Meanwhile, the Ministry of Health has revealed it has been contacted by Fiji's health authorities due to two people presenting positive for Covid-19 on day 12 testing in Nadi.
The two passengers had transited through Doha, Brisbane via Auckland on December 24 the Ministry said.
"There are robust procedures in place for passengers transiting through New Zealand at our airports. Transiting passengers remain airside at the airport and border staff apply the same precautions to them that they do to all passengers, including PPE, physical distancing and infection prevention and control procedures."
The Ministry confirmed that of the passengers from the Doha/Brisbane flight whose final destination was Auckland, all have completed managed isolation with no positive cases reported.
Medsafe is aware of reports about a number of deaths in elderly people in Norway who had received the Pfizer/BioNTech vaccine, today's statement said.
"It's reported that the deaths occurred in very frail patients who may have had only weeks or months to live, and that further investigation into these deaths will take place.
"We are closely monitoring this situation as well as the results of the vaccine rollout out in other countries, including reported reactions and the overall safety profile of the vaccine."
This includes the frequency of some reactions, the severity, and any previously unknown reactions and the monitoring will add to the clinical data the Ministry is expect to receive from Pfizer.
Medsafe will stay in contact with the European Medicines Agency as the vaccine rollout continues.
The Ministry of Health also confirmed that it would also continue working with Pfizer and other companies producing vaccines.
"As with all medicines, Medsafe will thoroughly evaluate the Covid-19 vaccines to make sure they are safe, effective and appropriate for use in New Zealand."
A spokesperson said "no vaccine will be made available for public use in New Zealand until it has completed Medsafe's assessment process and been approved as safe for use here."
The Ministry of Health has also revealed that it has been looking into the role of saliva PCR testing as part of further strengthening the Government's existing testing regime at the border.
"In parallel, ESR is about to commence saliva testing of Air New Zealand aircrew as part of research into testing for Covid-19.
"This research, which complements current work underway with the Ministry, will be provided to the Ministry of Health."
A Ministry spokesperson said that saliva testing is considered a "good additional option" for those who require frequent testing, such as border workers, where saliva-based testing can complement regular nasopharyngeal testing.
"Using the PCR nasopharyngeal swabbing method is considered the gold standard for Covid testing as it detects the virus the most effectively.
"Border workers in New Zealand will continue to be tested on a regular, routine basis with the nasopharyngeal swabs due to their high sensitivity in detecting the virus."
On Sunday, 1868 Covid-19 tests were processed. The seven-day rolling average up to yesterday is 3513 tests processed.
