Irish language activists received a good hearing from DUP leader Arlene Foster during a meeting on Thursday, campaigners said.
A delegation from Conradh na Gaeilge was invited to discussions at Stormont.
President Dr Niall Comer said he hoped the unionist party would support an Irish language act.
He added: "The Irish language community have been waiting too long for the state to bring in legislation that will protect these language-related human rights - the talks period is almost over, and now is the time for action."
Mrs Foster has been meeting non-political advocates of the tongue to try and understand what makes them so passionate about it.
She was strongly criticised in February during the Assembly election campaign for making disparaging comments.
Dr Comer said: "I believe we got a good hearing and we are hoping that the DUP will support an Irish language act after contemplating what we discussed with them today."
Mrs Foster met Irish-speaking schoolchildren in Newry this week and said she felt uplifted.
She exchanged a few words in Irish with teachers as she left the meeting.
It is part of a DUP outreach effort launched amid efforts to restore powersharing.
In February the unionist leader said more people spoke Polish than Irish in Northern Ireland and declared the party would never agree to an act protecting the language, a key Sinn Fein demand in the negotiations.