Ms Davidson, who is gay, spoke out after Theresa May outlined a plan to seek a deal with the socially hardline party, which has 10 seats in the Commons, to prop up her minority administration.
In an apparent criticism of the plan, Ms Davidson on Friday tweeted a link to a speech she made in favour of marriage equality, with the message: “As a Protestant Unionist about to marry an Irish Catholic, here’s the Amnesty Pride lecture I gave in Belfast.”
Ms Davidson, who became engaged to partner Jen Wilson in May 2016, later told the BBC: “I was fairly straightforward with her (Mrs May) and I told her that there were a number of things that count to me more than the party.
“One of them is country, one of the others is LGBTI rights.
“I asked for a categoric assurance that if any deal or scoping deal was done with the DUP there would be absolutely no rescission of LGBTI rights in the rest of the UK, in Great Britain, and that we would use any influence that we had to advance LGBTI rights in Northern Ireland.
“It’s an issue very close to my heart and one that I wanted categoric assurances from the prime minister on, and I received (them).”
Northern Ireland is the only part of the British Isles where same-sex marriage remains outlawed.
The DUP has repeatedly used a controversial Stormont voting mechanism - the petition of concern - to prevent the legalisation of same-sex marriage, despite a majority of MLAs supporting the move at the last vote.
The party has often found itself embroiled in controversy over its stance on gay rights issues.
Founded on the evangelical principles of the late Ian Paisley’s Free Presbyterian church, Northern Ireland’s largest political party has been repeatedly at odds with the region’s LGBT community.
Their differences highlight Northern Ireland’s often stark dichotomy between religious-based social conservatism and secular progressive liberalism.
While the party insists it is protecting the “traditional” definition of marriage, critics have denounced its stance as homophobic.
Going back decades, the DUP was at the vanguard of the failed Save Ulster from Sodomy movement that campaigned against the 1982 legalisation of homosexual sex in Northern Ireland.
In more recent times, former first minister Peter Robinson’s wife Iris, then an MP, described homosexuality as an “abomination”, while the MP son of Dr Paisley, Ian Paisley Jr, said he felt “repulsed” by homosexual acts.
A party councillor in Ballymena reportedly claimed Hurricane Katrina, which killed more than 1,500 people in the US, was God’s revenge for New Orleans hosting an annual gay pride event.
Former DUP Stormont minister Edwin Poots once hit out at a gay rugby team in Belfast, accusing it of introducing a sporting “apartheid” against heterosexual players.
Mr Poots also ended up in court for upholding a ban on gay men giving blood and, in a separate case, objecting to gay couples adopting. In the former case an appeal judge overturned a finding that he was motivated by bias.
In the 2015 general election campaign, DUP health minister Jim Wells resigned amid a controversy about remarks he made about same sex couples.
Defending her party’s stance on gay marriage in a recent interview, leader Arlene Foster insisted those who characterised the DUP as anti-gay were wide of the mark.
“They are wrong and they need to understand why we take those positions from a faith point of view and why we want to protect the definition of marriage,” she said.
“I could not care less what people get up to in terms of their sexuality, that’s not a matter for me, when it becomes a matter for me is when people try to redefine marriage.”
Conservative former Northern Ireland secretary Owen Paterson told BBC Radio 4’s Today programme: “I don’t see many major social issues coming up in the next parliament.
“You might get a debate I suppose on further reduction of abortion times as medical science advances.
“But the stuff you mention like gay rights and all that, which you’re probably referring to, that is all devolved.
“It’s not only a free vote issue, most of this, but it’s nearly all devolved and that’s down to the politicians in Northern Ireland to resolve.”
Told of Ms Davidson’s concerns about the potential reversal of gay rights, Mr Paterson said: “No, I don’t see that at all.
“She’s perfectly fair to raise it ... these issues are devolved, and if they were sorted in the UK Parliament they’d be free vote issues. I really don’t see them colouring the talks.”
Mr Paterson instead suggested the focus would be on Brexit.