UUP leader Robin Swann and Upper Bann MLA Doug Beattie have met representatives of the Irish language sector at Stormont.
Mr Swann described the meeting as "frank and respectful" but added that his party remained unconvinced of the need for an Irish Language Act.
Last month, he described Sinn Féin's push for the introduction of an Act as "a Trojan horse" and part of an attempt to "balkanise" Northern Ireland.
Mr Swann, along with party colleague Doug Beattie discussed with members of Conradh na Gaeilge and Forbairt Feirste their frustration that the issue had become a "red line in the current talks impasse" and was "effectively being used to hold Northern Ireland to ransom".
While Conradh na Gaeilge welcomed the meeting and said the UUP had "shown that they respect the language and the spoken community", they urged the Unionists to reconsider their opposition to an Act and support "protection and language development legislation".