Irish language activists have claimed DUP leader Arlene Foster told them there would be "legislative provision" for Irish.
Claims involving new details of a meeting between a DUP delegation led by Mrs Foster and the Conradh na Gaeilge group emerged as the stalemate between the DUP and Sinn Fein over Irish remained.
Sinn Fein and the SDLP are demanding a stand-alone Irish language act which is supported by the campaign group Conradh na Gaeilge - while the DUP is prepared to facilitate Irish as part of wider legislation also embracing Ulster-Scots and the Orange tradition.
The stand-off is at the core of the failure to restore devolved government. Former health minister Edwin Poots last week made clear his party is not opposed "in principle" to legislative support for Irish.
But in a letter to the Irish Times, the campaign group's executive director Dr Niall Comer said that in their meeting "the DUP delegation, and Mr Poots himself agreed that the costs of the proposals were in fact 'reasonable', and the party leader accepted there would be 'legislative provision' for the Irish language".
The letter said that if the DUP genuinely believes that "anyone who speaks and loves the Irish language is as much a part of Northern Ireland life as a collarette-wearing Orangeman" it should accept a stand-alone act.
This, it added, was "as recommended by the United Nations, the Council of Europe, the Dail and a majority of MLAs" - although the DUP used the Assembly's 'petition of concern' to block it.
Both Mrs Foster and Mr Poots have spoken briefly in Irish in recent weeks, gestures which have been welcomed by Irish campaigners.
The DUP last night said it wanted to make no further comment at the moment.