The Ulster Unionist Party has indicated it will take part in talks this week to try to resolve the crisis at Stormont.
They will meet the NI Secretary on Monday "to satisfy ourselves of the proper conditions for our full engagement in the new talks process".
The crisis was sparked by the murder of a former IRA man last month and the impasse over welfare reform.
On Friday, the prime minister called on the five main parties to take part in talks to try to resolve the crisis.
In a statement on Sunday, the UUP said: "The Ulster Unionist Party will enter talks, all things being equal.
"We have imaginative ideas, including the pathway to unblocking welfare, which we proposed at the talks last week.
"The status of the IRA and Sinn Fein's denial must be addressed as a matter of urgency, not relegated to the bottom of the agenda, as it was this week.
"We will meet the secretary of state early on Monday to satisfy ourselves of the proper conditions for our full engagement in the new talks process."
The crisis followed the killing of Kevin McGuigan Sr and the chief constable's assessment that members of the IRA had a role in the murder, and that the organisation still existed.
Last Wednesday, Bobby Storey, a former IRA prisoner, who is currently the northern chairman of Sinn Féin, was one of three senior republicans arrested over the murder. All were later released without charge.
On Thursday, DUP leader Peter Robinson announced he was stepping aside as first minister and that other DUP executive ministers would resign.
He asked his party colleague Arlene Foster to take over as acting first minister, after the DUP failed to get enough support to adjourn the assembly.
The Ulster Unionists had said they would not return to talks unless the Provisional IRA's existence was the first item on the agenda.
Also on Sunday, Ulster Unionist leader Mike Nesbitt said: "The IRA has established a crime empire with tentacles which stretch across the border into the Irish Republic and beyond this island.
"The government needs to show the resolve to confront paramilitary criminality in our society and remove it, once and for all."