Andrew RT Davies has quit as leader of the Conservative group in the Welsh Assembly after seven years in charge.
He had been criticised within the party for suggesting firms like Airbus were undermining Brexit by warning they could close UK plants.
Theresa May said the Welsh Tories had been a "strong voice for the people of Wales" under his leadership.
Interim leader Preseli Pembrokeshire AM Paul Davies told BBC Wales he wanted to take over permanently.
He has been backed by Monmouth AM Nick Ramsay, runner-up in the 2011 leadership contest.
Paul Davies said: "I've made it absolutely clear in the past that if there was a vacancy I would be interested in the post.
"We had a very frank and open discussion this morning," he said of Wednesday's group meeting with Andrew RT Davies.
"He heard the views of members, he reflected on those views and he decided that it was best to leave it to somebody else to lead the group."
The AM for Preseli Pembrokeshire said Andrew RT Davies had done a "fantastic job" as leader, showing "huge energy, huge dedication, huge commitment".
On Friday, Andrew RT Davies had accused Airbus - which employs more than 6,000 people in Flintshire - of "hyperbole" in making "threats" to leave the UK because of fears that Brexit would hit trade.
Guto Bebb, a Welsh Conservative MP and UK defence minister, condemned Mr Davies for making "inflammatory" remarks.
He also disputed Mr Davies's title as leader of the Welsh Conservatives - rather than its assembly group - and said he did not speak in such a capacity.
Andrew RT Davies factfile
- Born in Cowbridge, Vale of Glamorgan 1968 - aged 50
- Married with four children
- Partner in the family farming business near Cowbridge
- Joined the Welsh Conservative Party in 1997
- Stood as a general election candidate in 2001 and 2005
- First elected to the Welsh Assembly in 2007
- Served as party spokesman on health, education and transport
- Elected as assembly group leader in 2011
In a statement, Mr Davies said he was resigning as leader of the assembly group with "deep regret" following a group meeting on Wednesday.
The South Wales Central AM said it had been a "huge privilege to serve in this position since 2011, after securing the mandate of the party in a ballot of the membership".
"I look forward to supporting whoever emerges from the contest to replace me, and I will continue to place all of my efforts into advancing the Welsh Conservative cause both here in Wales and Westminster," he added.
Paying tribute to Mr Davies, Prime Minister Theresa May said: "Under Andrew's leadership, the Welsh Conservatives have provided a strong opposition to Labour in Cardiff Bay and a strong voice for the people of Wales, both at home and in Westminster."
'Larger than life'
First Minister Carwyn Jones said Mr Davies was a "decent and honest politician".
"Andrew has made his mark in Welsh politics, and his jovial and larger-than-life personality has always been a breath of fresh air during assembly proceedings," he said.
During his seven years leading the Conservatives in the assembly, Mr Davies appeared to be at odds with the wider party on a number of occasions.
In the 2016 referendum on Europe he backed Brexit while the then Prime Minister David Cameron campaigned to remain in the EU.
Some Tories were critical of Mr Davies for welcoming into the Tory assembly group ex-UKIP AM Mark Reckless - a former Conservative MP who had dramatically defected to UKIP on the eve of the Tories' 2014 party conference.
Mr Davies also denied reports of a spat with Welsh Secretary Alun Cairns over who should represent the Welsh Conservatives in TV debates in the 2017 general election campaign.
After the party then lost three Welsh seats in the June poll, he called for more clarity on who should be designated leader of the Welsh Conservatives.
Reacting to news of the resignation, Mr Cairns said: "Andrew RT Davies has played a vital role in holding the Welsh Labour government to account in the Welsh Assembly since 2011.
"As leader in the assembly he has a robust record of highlighting how a Welsh Conservative government could deliver a stronger Welsh economy."
Former Welsh Secretary Stephen Crabb backed Paul Davies for the leadership and suggested he would be open to working with Plaid Cymru in a coalition.
He said: "He's got that kind of subtle set of skills which means that he's able to work with other political parties.
"If there's one thing that Wales needs more than anything right now it's an alternative to just year after year of Welsh Labour government - and the only way you're going to get that is by getting the other parties to work together in the assembly."
Monmouth AM Nick Ramsay, who Mr Davies defeated in the 2011 leadership ballot of Welsh Conservative members, told BBC Wales he would not seek election this time around, but was calling on Paul Davies to stand.
The Preseli Pembrokeshire AM served as interim Conservative group leader in 2011 after Nick Bourne lost his assembly seat and until Andrew RT Davies was elected to succeed him.
Byron Davies, Welsh Conservative chairman, said: "It has been my pleasure to work with Andrew over the years and I would like to thank him for all that he has done as leader of the Welsh Conservative group in the assembly."
UKIP AM Neil Hamilton said he was sorry Mr Davies had resigned. "Andrew is a combative Brexiteer in a Tory group which is dominated by Remainers," he added.
Paul Davies said nominations for the permanent post of leader of the Tory group would "open in due course".
A Tory party source said AMs were in conversations on whether there should be more than one candidate for the role, and therefore a contest.
But one Conservative AM said there could be a "coronation".
Another party source alleged Mr Davies's resignation followed an "orchestrated plot from both ends of the M4", warning of "very dark times for Brexiteers".
Analysis by Aled ap Dafydd, BBC Wales political correspondent
Jovial and self-deprecating Andrew RT Davies is a "take me as I am" kind of man.
Not many politicians refer to themselves as "19 stone of prime Welsh beef" and I can't think of another would-be first minister who would allow me to film them eating a plate of chips for breakfast on the campaign trail.
In the latter stages of his seven years in charge there have been obvious tensions. As a staunch supporter of Brexit he came out on the winning side, a personal high point. But it made for a strained relationship with Downing Street.
Critical comments about Airbus's threat to leave the UK angered some of his Conservative colleagues.
If he thought something, invariably he said it or acted upon it.
A case in point was his sustained backing for the Swansea Bay tidal lagoon in the face of growing evidence over time that the UK government wouldn't be backing the scheme.
Earlier this year, Andrew RT Davies told me he'd be willing to step aside if it meant the Tories could form the next Government.
And so a pro-Brexit leader has made way and Remainer Paul Davies is his likely successor. That makes working with another party easier - even if forming the next Welsh Government is still a way off.