Peter Robinson had been under intense pressure since June to drop his support for the Maze peace centre – but only caved in after a series of last-minute secret phone calls with senior lieutenants in his party.
Sammy Wilson revealed he had a "frank exchange" with his leader in a telephone conversation in which he advised Mr Robinson to drop the party's strong public backing for the Maze centre.
The funding was scuppered by Mr Robinson's bombshell letter to his MLAs while he was on holiday, explaining why he could no longer support it.
Mr Wilson said speculation on the BBC that a "stand-up row" between himself and Mr Robinson led to the abrupt shift was wide of the mark.
"There was no stand-up row. I haven't met Peter since I was replaced as Finance Minister (June 29). I spoke to him on the phone," said Mr Wilson.
He added that Mr Robinson rang him in the first half of this week to consult him on the issue.
"I know he called other senior party figures because a couple of them told me – but I don't have a list and I am not aware of any meeting."
The East Antrim MLA denied that the call had been angry.
"Peter and I argue all the time but it is not heated. When you have known someone for the length of time I have known him, you can be dead frank with them. I was frank and told him what my views were. He was frank with me," said Mr Wilson.
He added: "One good thing about the relationship Peter and I have is that we can both speak our minds and we're fairly blunt. That's the way it should be – that's the way I like it."
Mr Wilson told Mr Robinson that the Maze centre would be "better put to one side".
"If it didn't have the confidence of the people who you needed to make this thing work then there was no point in proceeding. You would have had the irony of having a peace centre that was bathed in controversy and every time it was mentioned this whole controversy would be restarted," he said.
He believes that the DUP had put enough safeguards in place to ensure that the peace centre did not become what its opponents describe as a "shrine to terrorism". But it was also clear that many unionist victims' groups would not participate.
The two DUP veterans also discussed how a reversal of policy would be perceived.
"They will say it is a U-turn, it is surrender, it is caving in, it is weak and everything else. I told him that actually it was an indication of the strength of his leadership that he felt confident enough to do this," Mr Wilson recalled.
Mr Wilson denied that Mr Robinson originally intended to put his leadership on the line in a letter to party members backing the project.
"Tales of rows and so-called 'back me or sack me' letters are simply wishful thinking" on the part of those trying to undermine Mr Robinson, he said.
Mr Wilson said that since June, MLAs had been telling Mr Robinson that the Maze project was a political liability and work on it would be in full flow during the European election campaign.
Meanwhile, it has emerged that the board in charge of overseeing the Maze site's development is seeking urgent clarification about its future. Maze/Long Kesh Development Corporation chairman Terence Brannigan said: "The board agreed to ask the First Minister and Deputy First Minister to urgently clarify the situation."