The BBC said on Thursday it had "parted company" with the Radio 2 DJ because he had not co-operated fully with the Jimmy Savile sex abuse inquiry.
Mr Blackburn strenuously denies any wrongdoing.
The BBC said the corporation and Mr Blackburn were "clearly in disagreement on a range of issues".
The inquiry, by Dame Janet Smith, concluded that Mr Blackburn had been questioned by the BBC in 1971 about a complaint by a teenage girl. The DJ insists he was not.
Dame Janet Smith report: Key sections
Speaking to BBC Radio 4's Broadcasting House, in an interview to be broadcast on Sunday, Mr Blackburn said he had been told that by resigning "you don't cut off all ties, and we can probably bring you back in a few months".
But he said he had refused, adding: "I said: 'No I wouldn't do that, because I've got nothing to hide'."
Mr Blackburn said the inquiry - which looked into abuse by the late DJ Jimmy Savile and broadcaster Stuart Hall - included an accusation he had been among celebrities who had "seduced" a 15-year-old girl who later killed herself.
The 73-year-old denies the allegation and says he was cleared of wrongdoing.
Dame Janet said both senior BBC executive Bill Cotton and a senior lawyer said they had had conversations with the DJ.
She rejected evidence Mr Blackburn had given, in which he had said he had not been asked at the time about the allegation.
BBC director general Lord Hall said Mr Blackburn, who had most recently presented the Saturday afternoon Radio 2 show Pick of the Pops, "fell short of the standards of evidence that such an inquiry demanded".
But Mr Blackburn, who has said he will sue the BBC, where he worked for nearly 50 years, said he had told the truth.
"Now it's, I suppose, my word against a judge's - I've got no idea," he said.
"I was by myself, I told the truth, now if that's not up to BBC standards, I don't know what he [Lord Hall] means by that."
Mr Blackburn added that he wished he had been "investigated properly" in 1971 "because we wouldn't be in the mess we are now".
Mr Blackburn, who was the first DJ to broadcast on Radio 1 when it launched in 1967, also told the Daily Mail he would return to his job at the BBC "without any hard feelings" if he was offered it back.
He added: "If the BBC said: 'Let's wipe the slate clean and start again', I'd forget it. Absolutely.
"I'd shake the director general's hand and say: 'If the whole thing's been a mistake, let's say no more about it.'"
A BBC spokesman said: "Clearly Mr Blackburn and the BBC are in disagreement on a range of issues. Our position hasn't changed.
"As matters are potentially subject to a legal process, we have nothing further to add at this stage."
The full interview with Mr Blackburn can be heard on Broadcasting House on Radio 4 at 09:00 GMT on Sunday.
DJ Tony Blackburn has claimed he was offered the chance to resign from the BBC and return to work "in a few months", before he was sacked.