The DUP leader has proposed restoring Northern Ireland's Assembly and says in return she would bring forward proposals to address cultural issues, including the Irish language, in an agreed time frame.
Arlene Foster said she accepts that if those proposals could not command cross-community support, the Executive would fall and bring down power-sharing.
Her offer, made in a speech to party members in Belfast, is an attempt to end the political vacuum in Northern Ireland.
This has been in place since a row between the DUP and Sinn Féin collapsed devolved government last January.
It is not clear if Sinn Féin will be interested in the DUP offer as the party president, Gerry Adams, said yesterday there would be no Executive without agreement on the introduction of a standalone Irish language act.
The party’s leader in Northern Ireland, Michelle O'Neill, is due to give her reaction at 9am in Belfast tomorrow.
In her speech, Ms Foster said "we have nothing to fear from the Irish language nor is it any threat to the Union.
"We have previously supported practical measures for the Irish language and we will do so again if we can reach a wider agreement on these matters," she added.
There is no indication in Ms Foster's speech that she is prepared to change her opposition to a standalone Irish language act, but she does give undertakings to address the concerns of the Irish language community.
The British and Irish governments have been attempting to encourage the parties to agree compromises that would allow the return of power-sharing.
Politicians from five of Northern Ireland's parties have declared their support for an Irish language act, saying a majority of politicians at Stormont now support rights being enshrined in legislation.