Mr Robinson’s tactic, which has prevented an early move towards fresh elections, came after parties rejected a DUP proposal to adjourn the Assembly.
The DUP leader announced he would stand aside after failing to get support from other parties to suspend the assembly.
Arlene Foster will remain as finance minister and become 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”. Robinson’s Democratic Unionist Party, which favors continued United Kingdom membership, is the largest in the assembly.
The arrest yesterday of senior Sinn Fein official Bobby Storey, one of three men held over the shooting of Kevin McGuigan in Belfast last month, raised tensions.
Prime Minister David Cameron is said to be “gravely concerned” about the situation and a Downing Street spokeswoman said he was phoning Mr Robinson and Northern Ireland Secretary Theresa Villiers to discuss the situation.
Northern Ireland’s parties are being called into talks next week to resolve the political deadlock in Stormont.
Mrs Villiers will again be joined by the Irish Foreign Minister Charlie Flanagan, who has said: “There is a solemn duty and obligation on the part of everybody involved to forge agreement”.
The Sinn Fein leader was speaking after Mr Storey, the party’s northern chairman, was freed unconditionally by police.
McGuigan’s family and other republican sources in the city dispute this, and say members of the mainstream IRA carried out the murder in revenge for Davison’s death.
In London, Cameron said Friday he was extremely anxious about the political crisis in Northern Ireland, where the power-sharing government is on the brink of collapse in the gravest crisis since a 1998 peace deal ended years of sectarian violence.
Claims the IRA carried out the killing of one of its former members last month led to DUP members calling for Sinn Fein ministers to be excluded from their posts.
On the suspension of the Assembly and political institutions, Ms Villiers reiterated she did not believe it was the right thing to do at the moment although noted all options would be kept open if circumstances changed ” dramatically “.
Unionists argue that Sinn Fein, a republican party, should be excluded from government if the IRA is still active.
He said power sharing was “fledgling, hard but still better than war”.
“If this action by the DUP is intended by them to create space for talks to begin next Monday, we will certainly do everything in our power to make that work”, said Martin McGuinness, deputy first minister of Sinn Fein.
“I think it would send a very negative message and would be rist to the mill of those who in the past have tried to plunge us back to the past”, McGuinness said.