Simon Bridges has put his hand up for the National Party leadership, while Amy Adams is also due to explain her intentions this afternoon.
Adams - considered a contender if she puts her hand up - has scheduled a press conference for 3.30pm today.
In an announcement at Parliament this morning Bridges said he believes he is the right person to lead the National Party to victory in 2020, bringing experience as well as a generational change.
"I'm 41, I have a young family," said the MP for Tauranga, who has held a broad range of portfolios.
"Many colleagues have come to me to talk to me about it, and I feel [I have] strong support from the caucus."
He said the party needed to renew and refresh, and to represent its principles, including individual freedom, personal responsibility, competition, strong families and security.
"I'm pretty excited about this. I'm looking forward to the next two weeks.
"We do have to replace our leader, so a number have come to me. I've got good support."
Bridges paid tribute to departing leader Bill English in Parliament this morning, saying he learned a lot from him, and said he had the highest regard for others who may seek the leadership, including Amy Adams and Steven Joyce.
Judith Collins, who also announced her candidacy this morning, was a "great person" who brings a lot to caucus, he said, and no matter what happens, she should be part of the National team.
But he was focused on his own campaign.
Bridges said Labour lacked a strong plan when it was in Opposition for nine years and he didn't want National to make the same mistake.
"We are the strongest political party in New Zealand but we will need to evolve and make sure we have fresh ideas so that we are ready to be in Government in 2020."
However, he did not want to outline his policy priorities: "I just don't think today is the day for that."
He also believed being Maori meant he had broad appeal.
"I understand my whakapapa. As a minister, I've spent a lot of time with iwi. This is something I understand the interest in."
Bridges is considered a front-runner for the National Party leadership.
Rodney MP Mark Mitchell said he is actively considering the leadership, but is yet to formally put his name forward.
Northcote MP Jonathan Coleman, who has put his hand up for the leadership before, said he isn't ruling anything in or out at this stage, and deputy leader Paula Bennett has said she wants to stay deputy, but will not be seeking the leader position.
Auckland Central MP Nikki Kaye has ruled herself out for the leader or deputy leader positions.
Collins was the first to confirm that she will contest the role as the jostling begins to replace Bill English as National leader.
Bennett said she believed her strength was in supporting the leader.
"It is in my role as deputy where I have the most to add. Our new leader will need help from an experienced, loyal deputy and I offer that.
Judith Collins confirmed this morning she will contest the role and Simon Bridges has also hinted that he will publicly put up his hand later today.
Jonathan Coleman has declined to rule anything in or out. Nathan Guy and Nikki Kaye have ruled themselves out of the leadership contest.
Bridges, considered to be a leading contender, said: "I am talking to colleagues and considering things. I may have more to say later today."
Collins confirmed on Twitter this morning that she will contest the leadership.
"I'm announcing my candidacy for Leader of the NZ National Party. We're going to need strong & decisive leadership if we're going to win in 2020. I'm that person," she said.
Collins said she was the best person to take on Prime Minister Jacinda Ardern, who was a "very, very formidable person".
"We need the strongest Opposition we can have. We certainly have the numbers but numbers don't translate into winning," Collins told Radio New Zealand.
"We are going to have to do better than just having the numbers."
Ardern was a formidable opponent, Collins said. "And we would be very foolish to underestimate her. I don't."
Collins had initially contested the leadership in 2016 but withdrew when it was clear English would win it.
She said she meant business this time.
"I intend to be here for the ballot. I'm not messing around, this is not tiddly winks – it's the toughest game in town.
"I'm not putting my hand up to secure some prize. I'm putting my hand up because I believe I'm the best leader for the National Party at this time."
Asked if she could work with NZ First leader Winston Peters in future, Collins said politics was a form of business and she would work with whomever the voters decided.
"You do what you have to do in politics, or else you're not relevant."
Meanwhile Coleman, arriving at Parliament this morning, said he had the ability to criticise the Government while being positive about the country - a skill mix Bill English has said is important.
"I think I have those skills, but actually there are other people in the caucus that have those skills. The most important thing is we get the leadership team that can lead us to victory in 2020," Coleman said.
"That has to be the overriding consideration, rather than people's egos. It's one thing to become the Leader of the Opposition, but it's important we have a National Party Prime Minister in 2020 and we can achieve that."
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Coleman, who has put up his hand for the leadership before, said it would be ideal to have a consensus in caucus.
"And that may emerge in the coming weeks, but at the same time, the caucus always has the right to have that vote, and sometimes it's better to have that vote and clear the air rather than go through a cycle of people, as Labour did.
"The country wants us focused on their concerns rather than National's internal battles.
"We're going to spend the next two weeks unfortunately having to focus on ourselves, and then after that we've really got to get behind whoever is the leader and their deputy, and go hard out for victory in 2020."
Asked if he would consider the deputy leadership, he said: "I'm not ruling anything in or out at this stage."
Those considering running to replace English are expected to start showing their hands from today, and are already canvassing colleagues before making up their minds.
Kaye has had some support in online polls but said she was not standing for either leader or deputy.
Kaye would not confirm if she was helping with Amy Adams' bid. "Over the next 48 hours I'm sure things will become clearer and I want time to talk to my colleagues."
She said she believed there was "huge talent" in caucus.
Others believed interested include Amy Adams, Bridges, Mark Mitchell and Coleman.
Mitchell has confirmed he is considering standing for the leadership but was yet to decide.
"It is a two-week process and we are on day one. So I am absolutely very carefully considering it but I haven't made a final decision yet."
He would talk to colleagues as well. But he ruled out standing on a "ticket" as a deputy.
"I'm not considering deputy at all. I'm looking purely at the leadership."
He said he had the personal attributes and character to build a cohesive team.
"And I think I've got enough life experience to understand the direction the country is going in and what we need to be able to realise our true capability as a country."
Mitchell would be going to Australia tomorrow for a few days to support his daughter, who was representing New Zealand in surf boat champs.
There is also speculation Steven Joyce might stand although he is unlikely to publicly put his name up unless he knows he has support.
English's deputy Paula Bennett is yet to say what her own plans are but may be considering it herself.
Some of the contenders could run on a ticket with a deputy.
The pack is likely to narrow down to two or three by the time caucus votes on it. That could be as soon as next week rather than letting it drag out, although English's resignation takes effect on February 27.
Those weighing it up were already talking to colleagues to assess support last night, but none would publicly comment yesterday, saying it was English's day.