Covid-19 Response Minister Chris Hipkins said he should know in about a week's time when the remaining Pfizer vaccines will be arriving.
The Ministry of Health has changed its timeline on when the general public will be vaccinated from "from July" to "from the end of July".
Covid-19 Response Minister Chris Hipkins said the change of wording on the ministry's website was "frustrating and ultimately a little premature".
"Our goal has been to get a secure delivery schedule with Pfizer for July onwards and hoping we'll be able to lock that in at some point in the next week or so and then we'll be able to provide more detail to New Zealanders on what to expect from July onwards.
"We can't lock that in until we know how many vaccines are going to be arriving each week and when."
"Someone changing the Ministry of Health's website wasn't particularly helpful, that certainly wasn't part of the plan and that's not something I was aware of until it was raised yesterday" - Covid-19 Response Minister Chris Hipkins
"The reality is nothing has changed at this point."
The intention was still to start vaccinating the general public in July, though at that point there would be quite a lot of group 3 - over-65s - still to finish as well.
Pfizer had been confirming delivery schedules and quantities about four weeks ahead of when the shipment was expected, he said.
The company had a contractual commitment to deliver the rest of the vaccines between July and September.
Remaining supplies were still expected by the end of September, spread over the three-month period, he said.
"We're still getting weekly shipments and we expect to continue to receive that but we're down to the tail end of what we have ordered for the first half of the year."
About 40,000 doses arrive on Monday, while 80,000 to 90,000 jabs were being done each week.
Just over 300,000 doses were in stock, and by the beginning of July the stockpile will be down to a small amount, he said.
"When you're administering more than are being delivered each week then obviously that stockpile starts to really go down."
There are enough doses for the high-risk categories of groups 1 and 2, and to make a start on the over-65-year-olds' group, but not to complete them.
"The schedule between now and then has always been the subject of negotiation with Pfizer" - Finance Minister Grant Robertson
Finance Minister Grant Robertson said the contract with Pfizer contained penalties if it failed to deliver promised vaccine doses, which he said he was confident wouldn't happen.
"The agreement we've got with Pfizer will have all of the doses we need to meet our goal of all New Zealanders over the age of 16 who want to be vaccinated, being vaccinated at the end of the year, but that means that we will get a delivery at the end of September essentially of the full lot," he told First Up.
"The schedule between now and then has always been the subject of negotiation with Pzifer and we don't have it all sitting there. We get it in batches and that dictates a little bit of the roll-out through late June through to July. But we're just on track to meet the goals that we have and Pzifer will meet their contractual obligations I'm sure and at the moment people are still being vaccinated...
"We've just got a period near the end of June and beginning of July where we're just making sure we'll get enough vaccines to be able to keep the programme rolling forward.
He said he believed the target of vaccinating all eligible adults in New Zealand by Christmas remained on track.
College of GPs medical director Bryan Betty said the government needed to be very open with the public and health staff about Covid-19 vaccine supply.
"There probably will be disruptions and changes in terms of timeframes ... that is just the reality" - Dr Bryan Betty
"We need to be realistic with the situation. We're part of a global supply chain, there's a lot happening around the world with Covid and I think there's a high risk of disruption to vaccine supply into New Zealand."