There have been calls for Mrs Robinson to step down from all elected roles immediatley
Northern Ireland's Deputy First Minister has said he was "shocked" by a BBC programme which made allegations about the First Minister and his wife.
Sinn Fein's Martin McGuinness said he is seeking an urgent meeting with First Minister Peter Robinson.
He said there are "implications" for the office of first minister and deputy first minister.
Downing Street has said that the prime minister would not comment on personal issues.
The Ulster Unionist Party have said "the appropriate authorities" will be required to investigate the claims.
The BBC Spotlight programme revealed DUP MP Iris Robinson broke the law by not declaring her financial interest in a business deal.
The programme also reported that her husband, First Minister Peter Robinson, became aware of the money she had received from developers.
The programme said while he pressed his wife to return the money, he failed to tell the proper authorities about the transaction despite being obliged to act in the public interest by the ministerial code.
The Ulster Unionist leader, Sir Reg Empey, said it was clear to him Mrs Robinson's position as an MP, MLA and councillor was "utterly untenable."
He said she should resign all her positions with immediate effect. Mrs Robinson has previously announced her intention to leave politics.
He added the programme had raised matters of "deep concern to all those concerned with the integrity of political life and the democratic process".
David Ford leader of the Alliance Party and Sinn Fein's Gerry Kelly agreed that Mrs Robinson should step down from all public roles right away.
Mr Ford also called on the BBC to give all the information they have to "the appropriate authorities."
Jim Allister, of Traditional Unionist Voice, said the issues raised in the programme must be addressed "with utter transparency and candour".
Dominic Bradley, a SDLP member of the Northern Ireland Assembly used his Twitter page to describe the the revelations in the BBC programme as "GUBU if ever there was GUBU" - that refers to an Irish political acronym which means "Grotesque, Unbelievable, Bizarre, Unprecedented."
The SDLP leader Mark Durkan said Mr Robinson's position as first minister is now "questionable."
The Shadow Secretary of State, Owen Paterson, said serious allegations have been made. He said they must be thoroughly investigated by the relevant authorities
Mr Robinson said on Friday comments and conclusions were made on the programme "without any supporting facts".
"While I have learned from Spotlight for the first time some alleged aspects of my wife's affair and her financial arrangements, I will be resolutely defending attacks on my character and contesting any allegations of wrongdoing," he said.
He was supported by his party colleague Edwin Poots, the Northern Ireland Environment Minister.
Mr Poots said the First Minister had done nothing wrong, and was a victim of what happened.
Sir Alistair Graham, the former chair of committee on standards in public life, said a major investigation into the allegations was called for.
"On the basis of these allegations it seems to me that, prima facie, there are grounds for a major investigation by the various commissioners who have responsibility for standards in Westminster and the Northern Ireland Assembly, and presumably at a local council level as well," he said.