"We're working hard on a strategy at the moment to accommodate that growth," she said.
That plan will be announced sometime next week, with sources promising everything is on the table.
New shipments of vaccine will continue to arrive each week, but the Government is concerned about the next four weeks in particular, where overwhelming demand for jabs could put pressure on supplies.
Details of the plan being worked out between the Ministry of Health and the Beehive include the possibility of getting some vaccine supplies early from Pfizer.
Given overwhelming demand for the vaccine around the world, it may not be possible to secure large shipments of additional jabs from Pfizer.
Another option is to swap with another country. That country would effectively lend New Zealand its vaccines in return for New Zealand sending doses to that country at a later date.
The Government wants these doses to be of the Pfizer vaccine, which is doing the heavy lifting of the vaccination rollout so far.
However, there is a possibility the jabs will be from different brands. AstraZeneca and Jansen vaccines have been given provisional approval by Medsafe in New Zealand, meaning their vaccines can be used here.
The Ministry of Health is also in the process of ordering syringes that make it easier to extract six or seven doses of vaccine from each vial, rather than just five or six.
This will make existing stocks go further.
The pressure comes off in October, when the country will receive nearly all of the vaccine it hopes to administer by the end of the year - roughly 4 million doses in total.
Currently, the country's vaccinators are administering about 420,000 doses a week, leaving only a small margin before each new shipment. The precise details of those shipments is commercially sensitive.
The National Party is keen for vaccinations to ramp up.
The party's Covid-19 spokesman Chris Bishop urged the Government to set a target of at least 100,000 doses administered per day.
To date, the rollout peaked at just over 90,000 doses a day.