Kate Forbes has said she felt “greatly burdened” that offence had been caused by her views on social issues.
Speculation had been mounting over whether the SNP leadership hopeful would continue in the race after a raft of party MSPs withdrew their support following her comments on equal marriage.
Ms Forbes, who is a member of the Free Church of Scotland, received a backlash after she revealed on Monday that she would have voted against same-sex marriage legislation if she was an MSP at the time in 2014.
She went on to say that she believes having a child outside of marriage is “wrong” according to her religious beliefs.
Ms Forbes took Wednesday off to regroup after the backlash and she has now pledged to defend the rights of all Scots.
Addressing the controversy, she said in a statement on Facebook and Twitter: “I feel greatly burdened that some of my responses to questions in the media have caused hurt, which was never my intention as I sought to answer questions clearly.
“I will defend to the hilt the right of everybody in Scotland, particularly minorities, to live and to live without fear or harassment in a pluralistic and tolerant society.
“I will uphold the laws that have been won, as a servant of democracy, and seek to enhance the rights of everybody to live in a way which enables them to flourish.
“I firmly believe in the inherent dignity of each human being – that underpins all ethical and political decisions I make.”
Ms Forbes also said her Skye, Lochaber and Badenoch constituents are in “full knowledge” of her religious views and are “comfortable” knowing she would serve “faithfully and without prejudice”.
She added: “It is possible to be a person of faith, and to defend others’ rights to have no faith or a different faith.”
It comes as the Free Church of Scotland condemned the “anti-Christian intolerance” it claimed had been shown to Ms Forbes.
A church spokesperson declared: “Kate Forbes is standing on the basis of her policies – the fact that she is being criticised for her Christian convictions shows a level of bigotry that has no place in a pluralistic and diverse society.”
In a shift away from the conversation around her personal beliefs, Ms Forbes went on to outline key details on policy, which she vowed would see SNP party members become “more engaged in policymaking than ever before”.
She said: “The role of our party – its members – is crucial to our success. Our membership is large. Our members are in constant contact with their fellow citizens.
“They know, better than anyone, what motivates those who support independence, and what holds back others whose support we need. In short they are in touch. Our members have experience and talent. Central to my plan is that they become more engaged in policymaking than ever before.
“The party making policy through a number of key committees would not exclude ministers, MSPs and MPs, as they have much to contribute. But so have the ordinary members, and it is their hand on policy that I want.”
Ms Forbes is running against Scottish Health Secretary Humza Yousaf and former community safety minister Ash Regan for the leadership.
Ms Regan confirmed to journalists on Thursday that she has enough nominations to progress in the contest.
She will formally launch her campaign on Friday, hours before nominations from SNP party members close.
Mr Yousaf and Ms Regan have publicly stated their support for same-sex marriage following the comments from Ms Forbes.
