National MPs are rejecting Labour's claims that a three-way leadership contest is a sign of conflict within the party.
Deputy Prime Minister Bill English, Police Minister Judith Collins and Health Minister Jonathan Coleman have all put themselves forward for the party's leadership, after Mr Key announced his resignation on Monday.
MPs will choose from the contenders - and anyone else who might put their hat in the ring - in a special caucus meeting on Monday. A candidate needs the support of at least 30 MPs to win.
Most of the 59 National MPs are refusing to say who they are likely to back.
Labour said the contest had ripped the lid off simmering divisions within the National Party caucus.
"This new situation - and I think you're going to see a bunch of people putting their hands up - it's almost certainly going to divide them," said Labour MP Phil Twyford.
Mr Twyford said the contest would be an interesting spectacle, particularly with the inclusion of Judith Collins.
"Judith clearly wants the job and I think there will undoubtedly be some people in the National caucus who do want to see Judith, the right wing of the caucus, make a run."
"I would not be here, still in the job, and putting in every effort that I possibly can if I didn't believe I was adding value.
"We're going to go into the toughest campaign ever that we have fought. I know that we need to win and the only way we can do that if we have some of the toughest people running it," Ms Collins said.
National leader will have more caucus support than Leader of the Opposition - Joyce
Economic Development Minister Steven Joyce said a leadership contest was a reality, not a sign of disunity.
He said whoever finally got the role would have the full support of caucus.
"We can be sure that whoever it is, they will have more caucus support than the leader of the opposition," Mr Joyce said.
Mr Joyce said other contenders may yet come forward and he wouldn't say whether he'll be one of them.
Most backbench MPs were reluctant to say what they thought of the contest and who they would back.
But Bay of Plenty MP Todd Muller said they would be weighing up between stability of the party and refreshing it.
"We're all going to reflect on what is the appropriate mix of our Prime Minister and Deputy Prime Minister against that criteria."
He said he wouldn't describe the contest as a sign of simmering tensions within the caucus.
Mr Muller said the news that Mr Key was resigning came as a bombshell and many were simply reflecting on that.
"Everyone at their own pace reflects on what the consequences are for the party, for the caucus and the direction of the government."
Two-thirds of National's caucus have not gone through a leadership change before and MPs can throw their name in the hat at any point until Monday's vote.
Parties consider implications of leadership change
Green Party co-leader Metiria Turei said National had a strange process to decide its leader.
She said it was up to them how they do that - but all of the contenders had similarities.
"They're all going to be leading a National government that has caused harm to families, that has left families homeless and that has increased child poverty in this country."
Māori Party co-leader Te Ururoa Flavell said the Māori Party would work with whoever takes up the leadership.
"That agreement stands on its own mana and we expect that any party that enters into agreement, as we did with National right from the very start, they've got to honour it, and I'm sure that they will do."
United Future leader Peter Dunne said confidence and supply agreements were between parties, not leaders.
The ACT leader David Seymour said his party's relationship with the government would continue, regardless of who the leader was.
"ACT has had four leaders during this relationship. National will now have had two. But the fundamentals that MMP requires continue," Mr Seymour said.