First Minister Arlene Foster is "open to meeting" with LGBT groups, her spokeswoman has said.
LGBT campaigners have welcomed the move, saying it would be their first meeting with a DUP leader.
It comes after Mrs Foster was urged by the Green Party's deputy leader to "reflect on" her lack of engagement.
Malachai O'Hara said the "time has long passed" for the First Minister to have sat down with LGBT groups.
He challenged Mrs Foster after she said it was "important that all communities have a voice in the political process".
Mrs Foster made the remarks as she defended her meeting with the Loyalist Communities Council, a group representing loyalist paramilitaries, to discuss concerns over the Northern Ireland Protocol.
In an interview with Belfast Live, Mr O'Hara said: "I think the time has long passed for the First Minister to have met with LGBTQ organisations."
The LGBT campaigner added: "There are issues faced by the community that need to be addressed, whether that's hate crime, access to IVF, risk of homelessness, health inequalities, poorer mental health etc - and the First Minister really needs to reflect on that, the fact that she has never met those organisations."
In response, a spokeswoman for the First Minister expressed her willingness to meet with LGBT groups.
"The First Minister is always open to meeting with representatives of all views and backgrounds, including further engagement with LGBT groups," she said.
"The Private Office has no record of any outstanding requests or invitations."
John O'Doherty, director of LGBT+ charity the Rainbow Project, welcomed the statement.
"We are pleased that the First Minister has indicated her willingness to meet with LGBTQIA+ groups and we will be seeking a meeting at her earliest convenience," he said.
"Consecutive Northern Ireland governments have failed to address the inequalities experienced by LGBTQIA+ people in Northern Ireland and we will be seeking concrete commitments on actions that government can take to improve the lives of LGBTQIA+ people.
"This would be the first meeting any Northern Ireland First Minister has had with LGBTQIA+ groups in Northern Ireland despite numerous requests from The Rainbow Project and others.
"We believe that a commitment to equality and equity for all across our society and will be seeking the same commitment from the First Minister."
Mrs Foster in 2018 became the first DUP leader to attend an LGBT event when she addressed a PinkNews reception at Stormont.
She said she valued the LGBT community's contribution to Northern Ireland, but asked people to respect her opposition to same-sex marriage.
But Mr O'Hara said the DUP leader had "effectively lectured at the community".
He said while Mrs Foster was entitled to her views on marriage, he criticised the DUP for repeatedly using an Assembly veto mechanism to block change.
Same-sex marriage was legalised in Northern Ireland last year after Westminster intervened during the Assembly's three-year collapse.
