Sinn Fein MLA Daithi McKay apologised "whole-heartedly" for his "inappropriate, ill-advised and wrong" contact with Jamie Bryson ahead of the blogger's appearance at the Stormont Nama inquiry
Mr McKay resigned and was suspended from his party over allegations he was involved in "coaching" loyalist blogger Jamie Bryson on his evidence to the inquiry.
In the wake of the allegations, the DUP called for a police investigation.
Following his resignation, Mr McKay said: "Shortly before lunchtime today I forwarded to the Assembly Speaker a letter of resignation from the position as SF MLA for North Antrim with immediate effect.
"Having reflected on the allegations against me which have arisen in the last 24 hours and consulted with associated, friends and family, I acknowledge and accept that my contact with a witness to the Finance and Personnel Committee's NAMA inquiry in advance of his testimony was inappropriate, ill-advised and wrong.
"I apologise wholeheartedly for this.
"Whilst I don't offer this in any way as a justification for my action, I want to be absolutely clear that my intention was not, as alleged, to coach the witness in question with regard to the substance of his testimony, but rather ensure that the inquiry had full access to the truth with regard to all the issues relating to the Nama scanda."
The controversy was sparked following leaked messages between Sinn Fein MLA Daithi McKay, who was chair of the committee, and another Twitter user believed to be in the party.
The inquiry was sparked following claims made in the Dail by Independent TD Mick Wallace, who alleged £7m in an Isle of Man account had been earmarked for a Northern Ireland politician or party.
A National Crime Agency investigation is ongoing into the allegations.
Sinn Fein, in a party statement on Thursday morning said the alleged contact happened "without the knowledge, involvement or sanction of Sinn Fein".
In a statement Martin McGuinness said the allegations were "profoundly disturbing".
He said: "If the allegations of inappropriate contact prove to be true, then Daithi McKay needs to seriously consider his position as an MLA.
"I want to state categorically that I had absolutely no knowledge of this exchange or contact.
"And having spoken to all relevant personnel in the Assembly I am now entirely satisfied that Sinn Fein had no knowledge of any such contact."
Loyalist flag protester and blogger Jamie Bryson was called to give evidence to the Stormont committee last September.
There was debate on whether his evidence should be heard with DUP members of the finance committee and Alliance MLA Judith Cochrane voting against his inclusion.
Mr Bryson's evidence at the committee named former First Minister Peter Robinson as one of five individuals due to share the sum, which had been moved from an Isle of Man bank account.
Mr Robinson who later appeared at the committee in October denied the allegations.
Leaked messages, seen by both The Irish News and the BBC Stephen Nolan Show, claim to show Sinn Fein MLA Daithi McKay, who was chair of the finance committee at the time, giving guidance to the loyalist blogger ahead of his appearance.
They show Mr McKay and Jamie Bryson exchanging direct personal messages on Twitter, the reports claim.
The Sinn Fein MLA then, it's claimed, advises Mr Bryson to follow a Twitter account in the name of Thomas G O'Hara who is understood to be a Sinn Fein party member.
It is alleged that messages of advice were then sent to Mr Bryson from that account on how to present his evidence to the committee.
Responding the DUP called for a police investigation and for Mr McKay to resign from his position as an MLA.
DUP MLA Peter Weir, speaking on Nolan, said: "I'm astonished and appalled.
"And if the allegations that have been carried today are shown to be correct and accurate I think it's the most scandalous breach of the position of a committee chair that I've seen.
"The actions have been highly innappropriate.
"It's about as devastating from the point of view of Mr McKay as it could get.
"It's important that Sinn Fein clarify the position of the party point of view. Who else knew about this and not disassociate themselves and to condemn but take action against Mr McKay.
"If it's shown to be accurate, it's difficult to get around that. I think Mr McKay's position as an MLA is untenable.
"I think he has to, if it's shown to be accurate he has to consider his position as an MLA off the back of this and resign.
"It's essentially a judge being in contact with one of the main prosecution witnesses."
Mr Weir called for a police investigation.
"This is something that will be referred to the standards commissioner I think there is also a question that the police need a level of involvement in this," he said.
"I think there is an argument if this is shown to be correct that there is a potential criminal offence.
"That is the scale of it and that is where the focus has to be.
"I think the police do need to investigate this. What we have seen is effectively a conspiracy between two individuals to abuse an inquiry on that basis it has potential of malfeasance of public office.
"And that needs to be taken absolutely seriously."
Sinn Fein, in a statement said: "Sinn Fein’s position has always been about getting to the truth about the sale of the Nama portfolio.
"Sinn Fein have only been made aware of these allegations today and if they are true, then this contact would be wholly inappropriate.
"If such contact did occur it was without the knowledge, involvement or sanction of Sinn Fein.
"Sinn Fein will pursue this serious matter urgently and robustly."