Ruth Davidson has been told by the prime minister that any Conservative deal with the Democratic Unionist Party (DUP) will not affect LGBTI rights.
The Scottish Conservative leader, who is gay, plans to marry her partner in the near future.
The DUP opposes same-sex marriage, with Northern Ireland the only part of the UK where it is not legal.
Ms Davidson said she had been given an assurance that gay rights would not be eroded in return for DUP support.
In a tweet sent on Friday afternoon, Ms Davidson highlighted a speech she made in Belfast about the importance of equal marriage.
She told the BBC’s Reporting Scotland programme that she had spoken about the issue with Theresa May on Friday evening.
Ms Davidson said: “I was fairly straightforward with her and I told her that there were a number of things that count to me more than party.
“One of them is country, one of the others is LGBTI rights.”
The Scottish Tory leader said she had asked for, and received, a “categoric assurance” from Mrs May that any arrangement between the Conservatives and the DUP would see “absolutely no rescission of LGBTI rights in the rest of the UK”.
And she said the prime minister agreed to try to use her influence to advance LGBTI rights in Northern Ireland.
Ms May, whose party lost its majority at Westminster in Thursday’s general election, says she will put together a minority government with the support of the DUP to guide the UK through crucial Brexit talks.
The DUP, which returned 10 MPs to Westminster, has garnered a reputation for its strong and controversial views on a number of social issues.
It opposes same-sex marriage and is anti-abortion – with abortion remaining illegal in Northern Ireland, except in specific medical cases.
In a short statement outside Downing Street after an audience with the Queen, Mrs May said she would join with her DUP “friends” to “get to work” on Brexit.
She referred to the “strong relationship” she had with the DUP, but gave little detail of how their arrangement might work.
It is thought Mrs May will seek some kind of informal arrangement with the DUP that could see it “lend” its support to the Tories on a vote-by-vote basis, known as “confidence and supply”.
When asked whether she was comfortable about the arrangement given the DUP’s views, Ms Davidson said there was “no suggestion” that the Conservative government would be dependent on the support of the DUP.
She added: “The prime minister has already made it clear that it is not going to be a formal coalition, so let’s see how the future days go ahead.”
Ms Davidson, who backed Remain in the EU referendum, has called for the Tories to listen to other parties to deliver an “open Brexit”, which she defines as ensuring that free trade is at the heart of the Brexit negotiations.
She said: “I want to make sure that Scottish businesses can trade as freely as possible with the other 27 countries in the EU as well as the other countries around the world.”
Ms Davidson’s party won 13 seats in Scotland as its vote surged across the country. Scottish Labour and the Liberal Democrats returned seven and four MPs respectively, with the SNP winning 35 – a drop of 21 from the 56 the party won two years ago.
Who are the DUP?
The DUP are pro-union (not Europe but UK), pro-Brexit and socially conservative.
The party, which returned 10 MPs to Westminster, has garnered a reputation for its strong, sometimes controversial views.
It opposes same-sex marriage and is anti-abortion – abortion remains illegal in Northern Ireland, except in specific medical cases.
One MP is a devout climate change denier, while a former MP once called for creationism – the belief that human life did not evolve over millions of years but was created by God – to be taught alongside evolution in science classes.
During the election campaign, the DUP’s Emma Little-Pengelly was endorsed by the three biggest loyalist paramilitary organisations.