Labour is calling for Transport Minister Gerry Brownlee to be stood down while authorities investigate his airport security breach.
Prime Minister John Key today stood by his decision not to accept Brownlee's resignation.
However, Key also refused to be drawn on whether his position would change if the investigation ended in Brownlee facing prosecution or other sanctions.
"That's not something I'm going to comment on today; let's just wait and see what the inquiry finds," Key told reporters.
Labour leader David Cunliffe said Key should ask Brownlee to hand in his transport warrant and stand him down for the duration of the Civil Aviation Authority investigation.
Brownlee yesterday delegated responsibility for the CAA to his associate minister, Michael Woodhouse, while it did its investigation.
But Cunliffe said that was not sufficient.
"It's not good enough for the minister to delegate the aviation portfolio to the associate minister. It's just not on to continue as transport minister while being investigated by transport officials.
"National ministers have to realise they are not above the law. All New Zealanders expect this investigation to be carried out without fear or favour.
"Mr Brownlee must face the consequences of his actions like any other New Zealander. Similar security breaches overseas have seen entire airports evacuated."
Brownlee offered his resignation yesterday after admitting he evaded airport security to board a plane with two of his staff.
He told Key he was in a hurry so had gone through an exit door after checking with an Aviation Security official that it was OK.
Key reiterated today that he considered Brownlee's action a "stupid mistake" and not a sacking offence.
"There's no question he's deeply remorseful for doing that. When I consider the actions of a minister and whether he is fit to be a minister I can't just do that in isolation [based on] one particular event ... as any employer would.
"He's been a great minister, got a lot of things right. Obviously, he had a bit of rush of blood to the head and made a mistake but I don't think that rules him out of being a minister."
Asked if people could have confidence in the investigation given that Brownlee was until yesterday the minister in charge of aviation security, Key said it would be conducted "completely independent" of Government.
"They will make their own decisions, their own findings, if there are repercussions for Mr Brownlee he will have to live with those, no-one is above the law."