Ian Paisley Jr has admitted he made "mistakes" in the controversy over his lobbying for constituency issues.
Ian Paisley Junior said the DUP did not use the matters as leverage
In the latest row, he has defended himself over claims he used the St Andrews talks to seek concessions.
The DUP MLA said the issue was "a distraction which has been blown out of all proportion". He refused to specify what blunders he felt he had made.
"Maybe I could have handled it better - everyone's clever with 20-20 hindsight," he told the Nolan Show.
It has emerged he was given a letter by government minister David Hanson during the October 2006 St Andrews talks, which laid the groundwork for the restoration of devolution in the following May.
In the letter, which was given to Mr Paisley on the final day of the negotiations, the government said the then-prime minister Tony Blair would look at a range of constituency issues, including the Giant's Causeway project, and would try to respond positively.
It was made public under the Freedom of Information Act by Traditional Unionist MEP Jim Allister, a former DUP member opposed to power-sharing who is currently contesting a by-election in Dromore, County Down.
The DUP has said in a statement that its party officers made it clear last October that none of the issues in the correspondence were raised by them "at any stage in the run-up to, during or after" the talks.
"They were not raised by or with the party, nor were they included on any shopping list considered and approved by the party officers.
"Jim Allister has confirmed that these issues were not raised at any of the meetings in St Andrews at which he was present - the party can confirm that they were not raised at any of the negotiating meetings at which he was not present."
Mr Paisley admitted on Wednesday he had made errors.
"If people feel I have embarrassed them, I have no problem in apologising to them as that was not my intention," he said.
"I think there have been mistakes - they were not intentional, I have been honest at all times in this."
He later said he had no intention of resigning as a junior minister.
The Giant's Causeway is Northern Ireland's top tourist attraction
Mr Allister had accused Mr Paisley of "wasting valuable leverage on securing concessions from the prime minister no less, not on matters of importance to unionists, but on issues of mere commercial or constituency import."
Among the issues raised was the Giant's Causeway project and it was suggested private sector land should be included in its development.
The letter also suggested dropping a judicial review of lands in Ballee.
The BBC reported in December that the case was settled after devolution in July.
The land is about to be sold by the Department of Social Development, for about £50m in a deal that involves a range of business interests, including Seymour Sweeney.
Mr Sweeney, a member of the DUP, is also the private developer seeking to build a new visitor's centre at the Giant's Causeway.
The Northern Ireland Office said a number of issues were raised with the government in the margins of the St Andrew's talks "that were not connected to the negotiations and, as is the usual practice, were taken away for consideration".
On Wednesday, SDLP leader Mark Durkan said what he called "the politics of side deals" was unacceptable.
Seymour Sweeney is seeking to build at the Giant's Causeway
"I think people can argue about where on the spectrum between stroke politics and sleaze Ian Paisley Jr is, but he's certainly on that spectrum," he said.
UUP deputy leader Danny Kennedy said the issues raised were of great public concern and should be subject to "immediate independent reviews".
Sinn Fein President Gerry Adams said Mr Paisley had "questions to answer about his relationship with Seymour Sweeney".
"When SF conduct our negotiations, our focus is on achieving for everyone that we represent, and even for those we don't represent," he said.