Health Minister Jonathan Coleman, Treasurer and Finance Minister Bill English and now Corrections and Police Minister Judith Collins confirmed they will run as National Party leader to replace John Key.
Deputy Prime Minister Bill English is the favourite given his endorsement from Key yesterday but said he was not taking a win for granted, even though he was well known in the caucus.
He did not nominate a possible deputy, saying that would depend on internal discussion.
Nor would he rule out standing on a ticket.
Read more:
• Bill English: Why I'm standing for Prime Minister
• Coleman: Why I decided to stand
• Next PM? Judith Collins joins race
He said two thirds of the caucus had not gone through a leadership change before and would want time to consider the options.
If he wins it will be English's second tilt as leader after he took National to a historic low in the 2002 election loss. He said he had learned a lot since then. "You learn more from losing than winning."
English said his focus was on the stability of the Government and economy.
Asked if he would offer something different from John Key, he referred to planning rules.
"There some areas I can see there are some opportunities."
He would not say if he would revise Key's promise not to change superannuation thresholds, saying Key had earned the trust of voters by sticking to that.
However he had not had any discussions about it himself.
Coleman said he was standing because he sensed "an appetite for change".
"Yes, I am interested. I would not put my hand out unless there was considerable appetite for a contest of ideas across the caucus," Coleman said.
"I've been taking some soundings - not doing numbers, but seeing what the appetite of caucus for a contest is.
"I sense an appetite in the caucus for change. "
Coleman would not name a possible deputy, but when asked if Amy Adams would provide the female and South Island balance said he would like to work with her.
He would not say if he know anyone else running.
Collins confirmed she would run for the top job on her way into the debating chamber this afternoon.
"As you know I've never been one to shy away from tough decisions," she told reporters.
"And today is a day that I've made a tough decision. And that's that I will be putting my name forward for the election ballot on Monday."
Collins said the 2017 election would be "an extremely hard-fought campaign".
Collins said the leadership position should go to the "best person for the job".
But she also underlined the different approach she would bring as a woman candidate, saying the National Party leader needed to connect to both men and women, as well as all ethnicities.
"And I believe I can do that."
She said National had been led by men "for quite some time".
"It will be really tough. We will be going in asking for a fourth term."
Collins has been in Parliament since 2002, representing National in the Clevedon and Papakura seats. She was previously the most senior woman in Cabinet but was demoted in 2014 after she was alleged to have undermined a senior public servant while serving as Police Minister.
Collins made her comeback last year, taking on the corrections and police portfolios.
MPs were in a high state of anticipation as they headed into Parliament this morning, although fevered lobbying has not yet begun.
MPs are expected to hear an emotional explanation from Key about his decision at this morning's caucus meeting, which will set the rules about the contest to replace him.
Social Housing Minister Paula Bennett will not rule out entering the leadership race.
Bennett repeatedly deflected questions about whether she would stand this afternoon, saying she would "just have my deliberations with the caucus".
Bennett is National's fifth-ranked MP and is the most senior woman in Cabinet.
She said she was "devastated" Key was leaving.
"He's the greatest leader I've ever known and ever seen and I'm just going to miss him. I'm going to miss him as a leader and miss him as a Prime Minister and miss him as a man."
Bennett would not comment on whether she would stand as deputy for English or Coleman. "I've got nothing to say. I'm just going to keep a bit of clear air."
Yesterday Key announced he was stepping down from Parliament and gave his backing to English to replace him.
Talking to reporters on the way into caucus this morning, Key said he would leave the caucus meeting for the discussion on the leadership contest.
He said he had spoken to English because he wanted to give him and his wife, Mary English, "a bit of time to mull it over".
Steven Joyce also would not rule out a bid for the leadership despite saying he had no leadership aspirations, AAP reports.
"I've never had much in the way of leadership ambitions and that hasn't changed. My job as I see it is just to serve New Zealand the best way," he said.
Maggie Barry, who only arrived back in New Zealand this morning after travelling to Mexico, said she was still in shock over the decision and the new leader would be a matter for caucus.
Asked about a growing mood for change in the caucus, Key said "that's always a view that people will take but you could also say there's been one way of meaning things for the past 10 years, that's been me and Bill, and it's been a pretty successful 10 years."
Education Minister Hekia Parata said she would back English.
"I'm not precluding that there will be a contest, I'm just saying I think he is best for the role of that's what he decides to put his name forward for."
She said English offered predictability and certainty and was known for his sound management of the economy.
"I think he's got a great set of values."
She would not say if anybody else had rung her or who she would back for deputy.
Backbench MPs were reluctant to say whether they would back English or whether there should be a contest.
But Bay of Plenty MP Todd Muller said he would welcome a contest.
He said it was too early to say if there was a mood for change "but I think there is probably an appetite for a contest so you can get a sense of where people intend to take the party over the next three years."
Justice Minister Amy Adams refused to say if she would put her name forward.
"It is something we will discuss in caucus and I'm not intending to play all that out in the media."
Transport Minister Simon Bridges has ruled himself out of the National Party's leadership race.
Bridges, who was among those tipped as a potential successor to Prime Minister John Key, said this afternoon he was "certainly not going for the leadership".
"What I'm making quite clear is that I'm not going ... for the position of leader of the New Zealand National Party."
Senior cabinet minister Gerry Brownlee and the party whips will be taking charge of the election process, including setting a deadline for nominations.
Brownlee said National had "a very very calm" caucus at the moment and members were showing a high degree of maturity.
National MPs who were willing to state their views were backing English.
They included ministers Michael Woodhouse and Nathan Guy as well as backbencher Nuk Korako.
Guy said English would be a "fantastic" leader and Prime Minister.
"Bill English has steadied the economy through some very turbulent times, he's got the history of the party, he's worked incredibly well with John Key, he's got broad support across the business community and I think quite broad support across the New Zealand public."
He would not put his name up for the deputy position, but expected numerous people would want to contest it. "I'm not in a team."
He said it was too early to tell what caucus would do - many were still coming to terms with Key's decision and it was the first leadership change for many.
Backbench MP Alfred Ngaro said it was something many National MPs had not experienced before because Key had led the party for a decade.
"So for us it will be a good chance to hear what happens. We don't know who's going to put their names forward. We've never been in this situation before so we are going to allow the process to take place and see what happens."
He said there was "lots of talk going on".
"At the moment we want to acknowledge the Prime Minister for his leadership and we will do that this morning within the caucus. And then the debate begins."
David Bennett would not say who he was backing, but said Key's views would influence the caucus.
Parmjeet Parmar also declined to give a position but said English was "great". She said her preferred leader was "definitely John Key. But he's leaving."
MPs also said they had been shocked by Key's announcement. Parmar said she had not expected it. "It was really shocking."
A recent UMR poll asked which MP people favoured to take over from Key should he step down - a question various polls have asked over the years.
English received the highest support at 21 per cent; Steven Joyce 16 per cent; Paula Bennett 11 per cent and Collins 6 per cent.
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