Arlene Foster has taken over as acting First Minister at Stormont after Peter Robinson stood aside.
Mr Robinson and the majority of his Democratic Unionist ministers are resigning amid an Assembly crisis in the wake of a murder linked to the IRA.
The DUP leader had warned that his ministers would quit if the Assembly was not adjourned or the British Government did not suspend the institutions.
The DUP step will not bring an immediate collapse of the Assembly institutions with executive departments still functioning under the temporary arrangements but the Executive will not meet.
The DUP wanted all Assembly business suspended to allow crisis talks to take place about the political consequences of the murder of Kevin McGuigan.
Mr Robinson's announcement came after Sinn Fein, the SDLP and the Ulster Unionists voted against a DUP proposal to adjourn the Assembly.
He issued his ultimatum on Wednesday after the arrest of three senior republicans, including Sinn Fein's northern chairman Bobby Storey, over the fatal shooting of former IRA man Mr McGuigan. The men remain in custody.
Police have said current members of the IRA were involved in last month's shooting of Mr McGuigan in a suspected revenge attack for the murder of former IRA commander Gerard "Jock" Davison in Belfast three months earlier.
The revelations about the IRA have heaped pressure on Sinn Fein to explain why the supposedly defunct paramilitary organisation is still in existence.
Mrs Foster, a Fermanagh and South Tyrone MLA, is the current finance minister and she will also continue in that role.
Mr Robinson said: "In light of the decision by republicans, nationalists and the UUP to continue with business as usual in the Assembly, I am therefore standing aside as First Minister and other DUP ministers will resign with immediate effect with the exception of Arlene Foster.
"I have asked Arlene to remain in post as Finance Minister and acting First Minister to ensure that nationalists and republicans are not able to take financial and other decisions that may be detrimental to Northern Ireland."
Northern Ireland Secretary Theresa Villiers said she would not be suspending the devolved institutions and called on the local parties to come together.
She said the DUP resignations would mean the functioning of the Executive became much more difficult.
"It is a sign of a complete breakdown in working relationships within the Executive."