Mark Drakeford in Welsh Labour bid to replace Carwyn Jones
Mark Drakeford has announced his intention to stand for the job of Welsh Labour leader, three days after Carwyn Jones said he would quit.
Mr Drakeford said he wanted to continue with the Welsh Government's "radical" tradition.
The Welsh Government finance secretary said: "I certainly had to think about it because it's an enormous job."
The first minister announced his intention to stand down in the autumn, on Saturday.
Meanwhile Hefin David has become the first AM to publicly back Health Secretary Vaughan Gething - who has not ruled himself out but has not announced he will stand - for the leadership.
Another Labour AM, Lee Waters, warned AMs from narrowing the contest to a "two-horse race".
Mr Jones, who has been first minister and Welsh Labour leader since 2009, said recent months had been the "darkest of times".
He had been under intense pressure since Carl Sargeant was found dead in November, days after Mr Jones sacked him from the Welsh Government.
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Mr Drakeford told BBC Radio Wales: "It [the job] takes a lot out of anybody who does it. It has an impact not just on their lives but the lives of their family as well.
"I've said many times that I've not had a personal ambition to be first minister, but I want to make sure that there is a choice in this election, a political choice.
"I belong to the centre-left of the Labour Party. I think it is very important that strand in the party has a candidate who can put themselves forward and that means that the many thousands of new members who we are lucky to have in the Labour Party will have a proper political choice in front of them and I think that's very important."
The 63-year-old said Mr Jones had done an "incredible job over a very long period" and had made a "courageous and mature decision that gives our party an opportunity now".
"My own political position is on the left of the Labour party and I think that as the party comes to a renew itself in the second half of the assembly term, parties of the left need to lean left, when it comes to renewal, that's when you find the new ideas, that's when you find the energy from all of our new party members to carry the party forward," he said.
"But I cannot possibly describe myself as some sort of insurgent candidate here. I have been part of the government in Wales almost since the start of devolution. I think we have done many radical things while we have been in government and I want to go on doing more in that tradition."
The AM, widely considered to be a front-runner, said it was important that there is a contest and said that the election cannot be conducted under the same electoral college as had happened for the deputy leadership.
He said he would see himself leading the party into an election and, if successful, to establish a government in the next assembly term.
But he suggested he would then stand aside for a "new generation of leaders to put themselves forward for election".
Analysis by Nick Servini, BBC Wales political editor
There was some striking honesty from Mark Drakeford as he announced his decision to stand.
Firstly, there was no attempt to reinvent himself in any shape or form in a bid to emerge from the relative shadows of the finance secretary role into the top job.
He says his strength is his experience and practicality. I think we can assume there will be no eye-raising promises being made in his campaign.
This should be a man who, above all, knows what is and is not achievable from a Welsh Government.
And secondly, he set out an unusually specific timeline, effectively saying that this contest has come too early for the 2016 cohort of new Labour AMs, but he will act as a bridge until the time is ready for them at some point in the next term.
Mr Drakeford made the announcement on the Good Morning Wales radio programme and is the first to declare his intention to run for the leadership.
He has already secured backing from senior Labour AM Jane Hutt, as well as Mike Hedges and Mick Antoniw.
Julie Morgan, Julie James, John Griffiths, Rhianon Passmore and Jenny Rathbone are also backing the leadership bid.
Any candidate will need at least five nominations from AMs, other than themselves.
Mr Drakeford, who has been a professor of social policy at Cardiff University, is on the left of the party and has been the Labour assembly group's most high profile supporter of Jeremy Corbyn.
He was born in Carmarthen but has lived in the capital for more than 30 years and been Cardiff West AM since 2011.
He served as as special advisor to former first minister Rhodri Morgan and, following his election, was appointed health minister in 2013.
The AM has served as finance secretary since the last Senedd election two years ago and has had a key role in the negotiations with the UK government over Brexit legislation.
On Tuesday Hefin David became the first AM to declare his support for Vaughan Gething to run for the leadership.
Vaughan Gething is among those who have not ruled themselves out of the race and is considered to be a likely candidate to run against Mr Drakeford.
Mr David said: "Vaughan is an engaging and inspiring presence in our politics.
"He has all of the necessary cabinet experience and will be best placed to unite and connect our communities in these turbulent times."
But Llanelli AM Lee Waters warned AMs that there needed to be more than a "two-horse race", and told BBC Wales that the race is already narrowing.
"There are already 29 of us. Already a third of the Labour AMs have committed themselves to one candidate, which means there is obviously not many people to go around to support other people," he said.
"I think we should have three or four candidates who can put forward different ideas to give the membership a maximum choice."
Labour does not have a divine right to rule," he said, adding: "We have to show people we have a vision for change."
Meanwhile Dr Dai Lloyd, Plaid Cymru AM, told a news conference on Tuesday that there "should be no long goodbye" for the first minister Carwyn Jones.
It echoes Welsh Conservative warnings that Mr Jones's decision to stand down in the autumn leaves the Welsh Government in limbo.
He said: "We can't be otherwise engaged in a contest to decide who the next first minister is when a lot of stuff needs doing now."
He said Mr Jones had been a "lame duck FM for a long time".
Dr Lloyd denied that a candidate seen to be supportive of Jeremy Corbyn's politics would present difficulties for his party.
He said Mr Corbyn has a "problem with devolution".
Andrew RT Davies, Welsh Conservative leader, said on Tuesday morning that Mr Drakeford's description of himself as on the "centre-left" was the "first time I've heard someone describe Mark as centrist in his outlook".
He said Mr Drakeford would not represent "a new chapter" but "business as usual".
"He was the special advisor to Rhodri Morgan when the health service was reformed twice in Wales, that did not deliver any meaningful impact on waiting times," he said.
"He was the minister who was deployed last Wednesday to defend the government's use of that letter in threatening court action against the assembly in debating the debate we tabled last week."
Meanwhile, Dawn Bowden, Labour's Merthyr Tydfil AM, has called for a woman candidate to be on the ballot paper.
On Monday, she had not declared support for any one candidate, although she said there was a "huge amount of talent in the group" and all of those named so far were "very strong potential candidates".
"I do think that we should be, at this point of where we are in our progress, having a woman on the ballot paper," she said.
"In terms of everything we do within the party, we try to promote gender balance."