Covid-19 Response Minister Chris Hipkins told Parliament there was no confirmed delivery timetable, but denied the Government was sitting on its hands.
"In the international market for vaccines at the moment, one doesn't just simply email out an order and say, 'Here's what I want and when I want it'.
"There is some discussion that is required with the suppliers, who at the moment are facing unprecedented international demand and do have a limited capacity to supply.
But he said the "series of agreements that [New Zealand] has had with Pfizer have always envisaged that when a paediatric dose was made available or developed - if a paediatric dose was made available - then New Zealand would want to have access to that".
National's Chris Bishop is calling for the minister "to move with urgency to sort the situation out".
"Vaccination for 5-to-11 year-olds can't come quickly enough, given every extra person vaccinated in New Zealand raises our overall level of protection.
"This week, an expert committee advising the Food and Drug Administration in the United States recommended it authorise the vaccine for 5-to-11 year-olds and the FDA is expected to do so very soon," said Bishop.
"Our current supply of Pfizer vaccine can't be used for children. The paediatric doses are one-third the dose given to adults and teenagers, and each vial contains 10 doses for the younger age group. The vaccine vials also have a unique label and different colour for the cap."
Other countries like Canada had "signed specific agreements" for the paediatric doses and while New Zealand's entitled to order, has not yet done so.
"To make matters worse, Pfizer has not yet applied for approval to Medsafe for paediatric doses," said Bishop.
"Chris Hipkins needs to jump on the phone to Pfizer straight away during the parliamentary recess and tell them New Zealand needs supply of paediatric doses and that he wants an application from them in New Zealand as quickly as possible.
"While he's on the phone he could also place an order for some Pfizer booster shots for New Zealanders aged 12 and above, which the Government still hasn't done."