First Minister Peter Robinson said he and fellow ministers from the pro-British Democratic Unionist Party (DUP) would resign unless the Northern Ireland Assembly is suspended following a meeting.
His comments came after a senior figure in Sinn Fein, which governs alongside the DUP and wants Northern Ireland to become part of Ireland, was arrested in connection with the shooting of a former IRA gunman last month.
Sinn Fein was the political wing of the IRA during some 30 years of sectarian violence known as The Troubles, which was largely brought to an end by a peace deal in 1998.
"The DUP has made it clear it will not be involved in business as usual," Robinson said.
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"If others want the assembly to function normally in spite of Sinn Fein's position, we will have reached the point where, as a last resort, we will take this final step."
The issue is set to be decided at a vote of the assembly's business committee Thursday at which the DUP will ask for the assembly to be adjourned.
If neither happens, the DUP is expected to walk away, potentially triggering early elections.
Sinn Fein's Deputy First Minister Martin McGuinness said the crisis was down to "inter-party rivalry" among unionist parties, adding that suspending the assembly would be a mistake.
"I think it would send a very negative message and would be grist to the mill of those who in the past have tried to plunge us back to the past," he told reporters.
Three men accused in the case later had the charges against them dropped.