Humza Yousaf has urged his party to judge candidates to replace him on their policies instead of their religious beliefs.
In his first interview since he announced his intention to resign as First Minister, Mr Yousaf called for unity within the SNP.
Former deputy first minister John Swinney and ex-finance secretary Kate Forbes are front-runners to replace him in the top job, but neither has announced their candidacy.
Mr Yousaf told BBC Scotland on Wednesday: “I would say to supporters of any candidate that we will gain nothing if we talk each other down.
“The only people who benefit from that are our opponents.”
The outgoing First Minister and SNP leader also said candidates should not be punished for their faith.
Ms Forbes and Mr Swinney have both said they are considering their options before announcing whether they will stand to replace Mr Yousaf.
Ms Forbes, a Free Church of Scotland member, narrowly lost to Mr Yousaf in the 2023 leadership election, winning 48 per cent of the vote.
She had faced a tough campaign after questions were raised over her stance on equal marriage and gender reform.
While Mr Yousaf is not endorsing a candidate, he made it clear “you can be a person of faith and be first minister”, as he has shown with his own Muslim faith.
He added: “What people will judge any potential candidate on are their policies, what they stand for, what they will advocate, what they might end up moving away from in terms of policy.
“That is the right discussion to have – not whether somebody of faith can be first minister.”
Mr Yousaf also told the BBC that relationships with the Scottish Greens were becoming “strained” before he abruptly ended the Bute House Agreement between the two parties last week.
He said some members of the SNP were unhappy about Green co-leader Patrick Harvie’s comments on the Cass Review – a report into gender services in England – in which he questioned the scientific evidence used.
In Scotland, new prescriptions of puberty blockers were paused while the Government considered how the review impacted services north of the border.
Mr Yousaf told the BBC: “I made it very clear my position and the Government’s position was on the Cass Review, but it is fair to say that of course those comments that were made by Patrick Harvie on the Sunday Show did upset a lot in my group.
“We co-operated well with the Greens for almost three years on a number of issues but it was clearly becoming strained, the Bute House Agreement.”
He said he felt it was going to be “a matter of days or weeks” until the powersharing deal with the Greens came to an end, however he added: “I accept fully the manner in which it was done clearly caused upset and therefore I’ve paid the price of that.”
