Sinn Féin president Gerry Adams has said implementing an Irish language act must be a bedrock of any future Executive.
It comes after DUP leader Arlene Foster on Tuesday said her party wants to see devolution back running as quickly as possible.
A date for the new phase of talks to save power-sharing is yet to be confirmed.
While attending a Conradh na Gaelige event in Belfast on Wednesday, Mr Adams said Irish language rights remain a make or break issue for power-sharing in Northern Ireland.
He commented: "Let's be very, very clear - there won't be an Assembly without an Acht na Gaelige. The DUP know that, the governments know that.
"I understand that there are elements within unionism who think that this is in some way threatening but it's a matter of whether we want this part of the island to embrace everyone.
"You don't have to agree with everyone but you do have to have a legislative basis for respect and that includes the Irish language act."