Humza Yousaf accused Kate Forbes of appealing to Conservatives in a heated TV debate.
The Health Secretary also claimed that Forbes' support among SNP members was "plummeting" while the finance secretary cross-examined him.
Forbes asked Yousaf why a YouGov poll from earlier on Monday found that she was more trusted than he was in every policy area.
She said: "Trust matters when it comes to winning elections... actually on every policy area, in every single survey of the public, I am more trusted to do a better job. Why do you think that is?"
Yousaf fired back that the finance secretary had appealed to Tory voters while losing support from her own party.
He said: "I've noticed actually in all of the polls, you've managed to appeal to Conservative voters the most.
"But among SNP members you've actually managed to drop support quite significantly.
"I'm not surprised that amongst Conservative voters and Conservatives, I'm not that popular.
"I'm a progressive who wants to break up the United Kingdom."
He added: "You started this race as the bookies' favourite, the runaway favourite, and now among the SNP support, you've managed to plummet.
"Your support and your ratings have dropped."
He also said that the polls said Forbes was more trusted because she had "a public service delivery" role when he had had "three of the most difficult [jobs] in Government".
He added that he wants "to promote a well-being economy that puts people at the centre" and that he would create a minister for small businesses.
The candidates were in South Queensferry for the Sky News debate for the third televised event of the leadership contest.
The debate was hosted by Beth Rigby, the broadcaster's political editor.
It came at an important time in the contest, as the ballots opened for the leadership election at noon on Monday.
It also came just hours after the YouGov poll showed that support for independence was at 39 per cent - its lowest in years.
The polling also showed that the majority of Scots believe that the candidates won't be as good as Nicola Sturgeon.
All three candidates said that the price of SNP support for a minority Labour government would be another independence referendum.
Labour leader Keir Starmer has said that he would not have a pact with the SNP, but he may need their support if his party do not win a majority of seats at the next general election.
Yousaf said: “Give us the power to hold a referendum, because our democracy and our voice should not be denied any longer."
Forbes also suggested that people should be allowed to seek conversion therapy if they want to.
The finance secretary initially described the practice as “abhorrent” but then said that it is the "choice" of the person if they seek the therapy. She refused to say that she would ban the process entirely.
Rigby asked Forbes several times if she would commit to an outright ban on conversion therapy as many LGBT groups argue that people should not be allowed to do it even if they want to.
“My commitment to you is to look carefully at it,” she said.
“What I’m not going to do, because I don’t think any government has done that yet, it is to precede the normal process of legislation.”
She added: “I think people should be allowed to live freely as they choose and I don’t think there should be conversion therapy in existence in Scotland.”
Asked if a gay man should be allowed to seek conversion therapy to change his sexuality, Forbes said: “Well, it’s his choice, but I do not think we should allow conversion therapy.”
The finance secretary added: “My position on this is that people should be allowed to live as they choose in a free, tolerant society, and I think the conversion therapy Bill should reflect that.”
Ash Regan was unable to give more details about her plans for Scotland to have a new currency "within a few months" of independence.
When asked what institutions she would need to set up a new currency, she said: "A central bank. And I'm going to start all the planning and preparation for that on the first day."
But when pressed that there were other institutions that were needed, she said: "That's the institution you need."
After being questioned several times, Regan eventually asked Rigby: "What institutions are you talking about?"
When the presenter then listed other institutions that may be needed, like an independent debt management office, Regan said: "I don't have the full intel on this at the moment."
Voting for the SNP leadership contest will close at midday on March 27. The winner will be announced soon afterwards.
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