Duty Minister Peeni Henare said the Government has been working over the summer period to stay on top of the new strains and the worsening global situation.
He said the Government would not hesitate to introduce more protections as necessary.
The latest actions it has taken include introducing day 0 testing for those from higher-risk countries, and from Friday, pre-departure testing before returnees from the UK and the US can enter New Zealand starting on Friday.
He said the government is "looking closely" at other long-haul routes.
Medical director of The Royal New Zealand College of GPs Bryan Betty told 1 News he's very concerned about the emergence of new virus strains.
He said the situation has changed rapidly over the last few weeks, with countries losing control over the virus.
"We need to think very hard about the number of people coming in from those countries that have lost control over this Covid variant. That may mean decreasing the number of people coming into the country from places such as the UK, such as the US, such as South Africa."
Meanwhile, epidemiologist Dr Michael Baker has also said that New Zealand might need to close its border to the United Kingdom if cases of the new variant there continued to surge.
"I am very concerned, and this is possibly the most dangerous phase we have been in since the August Auckland outbreak," he told the Herald.
The new strain forced the UK back into lockdown, amid fears its health system will become overwhelmed, while confirmed deaths in the country have exceeded 80,000.
Experts say the new variant in the UK might infect three people, as opposed to the old variant infecting two, meaning it would spread much quicker through the community.
Covid-19 data modelling expert Shaun Hendy shared a similar warning with RNZ, in that the highest level of New Zealand's lockdown levels would likely be needed if a community outbreak of either the UK or South African variant was found in New Zealand
"Level 3 was effective back in August ... but I think if you take into account the extra infectiousness of these new variants, level 3 is probably not strong enough."
Meanwhile, desperate Kiwis trying to secure a spot on New Zealand's managed isolation facilities have resorted to a new computer programme able to book vouchers as soon as they appear.
1 News said the new system has made about 20 bookings so far for people in the UK, Australia and South East Asia.
The creator of the system told 1 News he is not the only one doing it.
New Zealand has 4500 MIQ rooms in total but next month there are just over 4600 bookings, 1 News reported.
The Ministry of Business, Innovation and Employment said it overbooks because not everyone with vouchers will end up using them.
The National Party has urged the Government to speed up its vaccine rollout given the increased risk of the new variants devastating the UK and South Africa.
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.
Henare said New Zealand's situation is different to other countries as we currently have no community transmission.
"We are working hard to keep it this way and take nothing for granted.
"We expect to be in a position to start vaccinating frontline workers from April 2021, and the public in the second half of the year."
He said New Zealand's Medsafe is working closely with its Australian counterpart, the Therapeutic Goods Administration (TGA), regarding the data both agencies are receiving from pharmaceutical companies about the vaccines and any approval decisions made by Australia.
