Scottish Secretary David Mundell has said he wants the Democratic Unionist Party (DUP) to "change its position" on LGBTI issues.
Prime Minister Theresa May is due to meet DUP leader Arlene Foster on Tuesday to finalise a deal on propping up her minority government.
Mr Mundell, Conservative MP for Dumfriesshire, Clydesdale and Tweeddale, was reappointed Scottish Secretary in a post-election Cabinet reshuffle on Sunday.
He became the first openly-gay Conservative Cabinet secretary when he came out in January 2015.
Questioned on the DUP's stance on gay rights, he said he does "not subscribe" to the Northern Irish party's position.
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.
Mr Mundell told BBC Radio Scotland's Good Morning Scotland programme: "I don't subscribe to the DUP's position on these issues but the DUP will not be influencing these decisions within the rest of the United Kingdom.
"We're not in any way signing up to the DUP manifesto. Most of these issues are devolved to the Northern Ireland Assembly."
He added: "I would like to see the DUP change its position, and indeed Northern Ireland as a whole change its position, on LGBTI issues.
"Ruth Davidson has been very clear on that, she actually went out to Northern Ireland and set that out, so they can't be in any doubt where they stand on these issues.
"I think change is brought about, certainly in Northern Ireland, by persuasion, by people working together and the best way actually to achieve these is to get the Northern Ireland Assembly back up and running, and I hope that will also be possible."
First Minister Nicola Sturgeon said careful scrutiny of any deal with the DUP would be needed to guard against any rollback of equalities legislation and also raised concerns on the impact on the Northern Irish peace process.
Writing in the Daily Record, she said: "The Good Friday Agreement requires the UK Government to be an impartial broker between parties in Northern Ireland and it would be shameful if, in the Tories' pursuit of power, they jeopardised the chances of a return to devolved government in Northern Ireland."
Marco Biagi, who served as Scottish minister for local government and community empowerment, said Mrs Foster contacted him in 2015 urging changes to planned legislation.
He claimed the DUP leader – acting in her capacity as a Stormont executive minister – called for Scotland to exclude gay couples in the north from being able to convert civil partnerships to marriages in Scotland.
He said on Twitter: "When I was a minister DUP's Arlene Foster wrote to me asking us to curtail access of Northern Irish citizens to Scottish same-sex marriages.
"I said no. Specifically this was couples with prior Northern Irish civil partnerships, who couldn't switch for marriages in NI (or England and Wales)."
Mr Biagi said the exchange happened when the Scottish government was in the process of introducing the conversion procedure from civil partnerships to marriages.
