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Robinson will stand down for six weeks, lawmakers were told, as the pressure finally got to the first minister after calls mounted for him to go over the sex and politics row.
"As a father and a husband, I need to devote time to deal with family matters," said a drawn-looking Robinson in a televised statement, his voice breaking.
"I continue to contend I have acted ethically and it is particularly painful at this time of great personal trauma that I have to defend myself from an unfounded and mischievous allegation," he added.
His defence came shortly after Northern Ireland Assembly speaker William Hay told lawmakers that Enterprise Minister Arlene Foster has been asked to be acting first minister during his absence "with immediate effect".
And Foster, making a statement which had been expected to be made by Robinson himself, voiced confidence that he would return.
"Peter Robinson is going to clear his name and I have no doubt about that matter... me standing here is very much for a temporary period of time," said the 39-year-old mother-of-three.
Robinson's wife Iris, also a top politician, last week admitted having an affair with a then 19-year-old, Kirk McCambley, and securing 50,000 pounds (56,000 euros, $80,000) from two wealthy developers to help him set up a cafe.
Peter Robinson has denied any knowledge of the deal, which he would have had to report to parliamentary authorities, but there were calls for him to quit over the weekend.
The DUP's power-sharing partners Sinn Fein had tabled an emergency motion calling for Robinson to explain himself before the assembly.
Robinson's 60-year-old wife, who is expected to quit her seats in the Northern Ireland Assembly and Britain's House of Commons imminently, is receiving what he described as "acute psychiatric treatment" in Belfast.
She previously admitted attempting suicide and suffering severe depression.
The scandal is playing out against an already tense backdrop in Northern Ireland.
Power-sharing between ex-foes the DUP and Sinn Fein was under strain due to failure to agree on the transfer of policing powers from London to Belfast, the last stage of the devolution process.
British Prime Minister Gordon Brown said late on Monday he had spoken to Foster and urged lawmakers in the province to stay focused on governing despite the political firestorm.
"I urge all politicians in Northern Ireland, whatever the turbulence of recent events, to remain focused on the business of government," the prime minister said in a statement.
Irish Prime Minister Brian Cowen welcomed Peter Robinson's decision to continue working on "the crucial issue of devolution of policing and justice and his commitment to a successful resolution."
Robinson's conservative DUP, which is Protestant and wants Northern Ireland to remain part of Britain, has since 2007 shared devolved powers from London in an administration with socialists Sinn Fein, which is Catholic and wants the province to join the Republic of Ireland.
Their failure to agree when control of the sensitive issue of policing should be handed to Belfast has fuelled concerns that power-sharing could break down.
There are also fears of a return to sustained violence in Northern Ireland, where three decades of civil unrest known as The Troubles killed at least 3,500 people but was largely ended by the 1998 Good Friday Agreement.
Last year, two British soldiers and a policeman were shot dead in attacks claimed by dissident republicans.
In the latest incident Friday, a Catholic police officer was seriously injured after a bomb exploded under his car as he drove to work.
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