Scottish Health Secretary Humza Yousaf is leading the race to replace Nicola Sturgeon after former frontrunner Kate Forbes triggered a major row over her views on gay marriage.
Ms Forbes sparked a furore only hours after announcing her candidacy by telling an interviewer that her conscience wouldn't allow her to vote in favour of same-sex marriage.
A string of backers withdrew their support, including Public Finance Minister Tom Arthur, Children's Minister Clare Haughey and Health Committee convener Gillian Martin.
Finance Secretary Ms Forbes was hotly-tipped to take over from Ms Sturgeon following her shock resignation, and 24 hours ago was the 2/1 favourite.
But the row could prove costly, with bookmakers upping her odds to 5/2 as Mr Yousaf - who said he would "always fight for the equal rights of others" - overtook her at 2/5.
Just three candidates - including former community safety minister Ash Regan - have put their name forward to be First Minister after several high-profile figures including Angus Robertson ruled themselves out.
Ms Forbes told The Scotsman: "I would have voted, as a matter of conscience, along the lines of mainstream teaching in most major religions that marriage is between a man and a woman.
"But I would have respected and defended the democratic choice that was made.
"It is a legal right now and I am a servant of democracy, I am not a dictator."
A senior member of her campaign team later told Scotsman journalist Alexander Brown that she had "f***d it".
But Ms Forbes, a member of the socially-conservative Free Church of Scotland, said her leadership bid isn't over yet.
She told the BBC: "We have a large party membership, most of whom are not on Twitter.
"I understand people have very strong views on these matters. I think the public are longing for politicians to answer straight questions with straight answers and that's certainly what I've tried to do in the media yesterday. That doesn't necessarily allow for much nuance.
"My position on these matters is that I will defend to the hilt everybody's rights in a pluralistic and tolerant society, to live and to love free of harassment and fear."
She later told Times Radio: "I regret enormously the pain or hurt that has been caused because that was neither my intention, and I would seek forgiveness if that is how it's come across."
Addressing the controversy former, Tory leader William Hague said he didn't believe someone who opposed same-sex marriage could lead the Conservatives,
He said: "If you want to be a leader you have to decide whether you're accepting of what's become the national culture or not. And I think in those cases, it's very difficult to be a leader."
Health Secretary Mr Yousaf said he will "always fight for the equal rights of others".
Asked what he thought of what Ms Forbes had to say on same-sex marriage, he told the Good Morning Scotland programme: "It's for her to defend her views I've made my views very clear.
"I think my track record on equality issues speaks loud and clear.
"I'm a minority in this country, I have been my entire life and my rights don't exist in some kind of vacuum, my rights are interdependent on other people's rights and therefore I believe very firmly, in fact with every fibre in my being, that your equality is my equality, therefore I'll always fight for the equal rights of others regardless of who they are."
Mr Yousaf said in an interview with Andrew Marr on LBC that he would not legislate on the basis of his faith and is a supporter of equal marriage.
Ms Forbes has also said she would not have voted for the Scottish Government's controversial Gender Recognition Reform (Scotland) Bill in its current form.
Mr Yousaf has previously promised to stand by the Gender Recognition Reform (Scotland) Bill and challenge the Section 35 order from the UK Government which seeks to block the legislation.
Speaking on the BBC, he described it as "an attempt by the UK government to undermine the democratic will of the Scottish parliament" and suggested Westminster was trying to "stoke a culture war."
