New Zealand Rugby has criticised December's Rugby Championship schedule because it means players will be forced to spend Christmas in quarantine.
The All Blacks play Australia in Sydney on 12 December and would need to self-isolate for 14 days on their return home under coronavirus protocols.
Argentina and South Africa will also compete in the six-week tournament.
"We haven't agreed to this schedule and are disappointed at the announcement," chief executive Mark Robinson said.
"We understand the commercial considerations in the scheduling. However, the wellbeing of our people is an incredibly important factor in this also."
He added: "All our planning and scheduling was on the basis that the All Blacks' last match would be on 5 December to give our players and management time to get home, undertake the quarantine back in New Zealand and be with their families for Christmas."
New Zealand Rugby has now called on the tournament's governing body SANZAAR (South Africa, New Zealand, Australia and Argentina Rugby) and Rugby Australia to reschedule the fixtures, stressing it is "committed" to taking part in the competition.
"We know the scheduling of matches has been a complex and dynamic issue to work through," Robinson said.
"[But] we believe that there are other solutions within the Rugby Championship window."
SANZAAR chief executive Andy Marinos said they had "exhausted every other option" and the six-week schedule was already "pretty arduous".
He added: "We've got to be cognisant of player welfare but there's also player safety."
Rugby Australia says "formal" requests for a condensed five-week tournament were rejected.
"That being said no-one wants players and team management to be away from their families and in quarantine over Christmas," RA interim chief executive Rob Clarke said in a statement.
"Rugby Australia will do everything in its power to help assist New Zealand Rugby and the team in finding a reasonable resolution."
World champions South Africa's participation in the Australia-based tournament will depend on whether a government ban on international sporting competition is lifted.
Rugby Championship fixtures
Round one - Saturday, 7 November, Brisbane
Argentina v South Africa
Australia v New Zealand
Round two - Saturday, 14 November, Sydney
New Zealand v Argentina
South Africa v Australia
Round three - Saturday, 21 November, Sydney
New Zealand v South Africa
Australia v Argentina
Round four - Saturday, 28 November, Newcastle
Argentina v Australia
South Africa v New Zealand
Round five - Saturday, 5 December, Sydney
Argentina v New Zealand
Australia v South Africa
Round six - Saturday 12 December, Sydney
South Africa v Argentina
Australia v New Zealand