Nicola Sturgeon said SNP MPs elected in May would back any move at Westminster to establish such a diplomatic post within the Foreign Office.
Labour leader Ed Miliband announced last September that former EastEnders star and Labour peer Lord Cashman would be the party’s envoy on LGBTI rights.
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The US Department of State is also to announce the appointment of a special envoy to advocate for LGBTI rights overseas later this month.
Ms Sturgeon will today address a conference organised by Out for Independence, the LGBTI wing of the SNP.
Speaking before the event, she said: “Too many LGBTI people in too many countries still face the most extreme forms of prejudice and hate - our voice must be one of those arguing and advocating for equality, tolerance and love.
“That is why a team of SNP MPs elected in May will support the establishment of a special envoy, a diplomatic post within the Foreign Office, to promote the rights of LGBTI people throughout the word, as an integral part of UK foreign policy.
“I know that other parties, including Labour, advocate this move - just as there is action within the United States to create a similar post there - and I have no hesitation in working across party boundaries to bring it into being.”
The First Minister said that attending one of Scotland’s first same-sex marriages was among her proudest moments since taking up the post.
She added: “The stain of intolerance will not be removed entirely from our country or culture overnight - but by the laws and values we promote we can and will move ever closer towards the good society where everyone feels safe and valued and above all equal - regardless of sexuality or gender, race or religion, ability or disability.
“That is the vision of a One Scotland I am pledged to.”