By midnight Monday, 13,000 staff or volunteers must have had a first vaccine dose or be forced off the front line.
Minister of Internal Affairs Jan Tinetti said she was exploring options.
"Fenz have formally requested a temporary exception to the vaccine mandate," she said in a statement.
"As Minister I am exploring options to ensure that our communities are safe and that we have the firefighters we need.
"This includes the option of a temporary exception for a brief period of time."
RNZ understands Fenz has asked for a further two weeks.
The Professional Firefighters' Union warned that without an exception to buy time to prepare, emergency callouts would be hampered because crews could not go out understaffed.
"Any exception is absolutely imperative," national secretary Wattie Watson said.
"Otherwise on Tuesday, they will not be able to respond to the level or extent that they are now."
Workers were asked to tell Fenz their vaccination status by 5 November, but Fenz has not responded to requests for information on these numbers.
"We always have contingency plans in place so we can continue to serve our communities across the country," it said.
The agency this morning did not confirm it had asked for an exception. It said it would "continue to keep our people, and our Minister, updated as we work through all implications of this mandate. We are looking at all options available to ensure we reach a satisfactory outcome for our people and our communities."
The association that acts as a union for volunteer firefighters said it did not know how many might be ruled out of callouts by the vaccine mandate, and would not be finding out.
