John Prescott says he will not quit as deputy prime minister despite pressure over his meetings with the man hoping to turn the Dome into a super-casino.
Mr Prescott said he had regular talks with Dome owner Philip Anschutz but had no influence over decisions on casinos.
Cabinet Secretary Sir Gus O'Donnell has said the two civil servants who went with Mr Prescott to meet Mr Anschutz should have declared the visit.
And Parliament's standards watchdog is launching an inquiry into the affair.
Sir Philip Mawer is looking into complaints that Mr Prescott did not log the hospitality in the MPs' register of interests - something he has now volunteered to do.
He hopes to report to MPs before Parliament begins its summer break on 25 July.
Sir Alistair Graham, chairman of the Committee on Standards in Public Life, says Tony Blair risks facing serious criticism if he fails to deal personally with the Prescott controversy.
Meanwhile Sir Gus, responding to a letter from the Tory's culture spokesman Hugo Swire, said that the officials should have been advised to register the stay at the time the visit was made last July.
He added that he was satisfied that the failure to register had not affected their subsequent advice or actions.
Sir Gus also confirmed to Mr Swire that the two civil servants in questions were private secretaries but would not name them.
Sir Alistair said the prime minister should ask his adviser on conflicts of interest, Sir John Bourn, to look into the situation.
Downing Street refuses to say whether Mr Blair has asked Sir John or Cabinet Secretary Sir Gus O'Donnell to look into whether ministerial rules have been broken.
Mr Blair's official spokesman said Mr Prescott said had explained his meetings with Mr Anschutz and it was legitimate for him to meet with investors in regeneration projects.
Earlier, Mr Prescott attempted to defend his position in his first broadcast interview since his affair with his diary secretary Tracey Temple was revealed.
He apologised for that "mistake" but refused to say whether he had had other affairs.
"There is no truth in much of the stories that are made in the papers," he told Today.
He went on: "I know there is a media storm against me - they don't like me and to be honest, I don't like them."
The latest controversy centres on Mr Prescott and some of his officials staying at Mr Anschutz's Colorado ranch last July.
Mr Anschutz owns the Millennium Dome which is among the short-listed sites for the UK's first super-casino, allowed under the Gambling Act passed last year. A decision on the final site is due by the end of the year.
Documents seen by the BBC suggested the two men may have discussed plans to turn the London venue into a casino in 2004.
Mr Prescott says Mr Anschutz mentioned it once during their various meetings and he told the US tycoon he was not dealing with the issue.
The deputy prime minister says he did not know his department made a payment to charity in place of paying for the stay directly.
Mr Prescott told Today his American trip, which he has now declared in the register of interests, had been cleared by the senior civil servant in his department.
He said he had started receiving updates every six months from Mr Anschutz about the Dome in 2002.
But since then he had made sure he was separated from any planning decisions his officials took over the Dome.
The former Conservative leader of Southend-on-Sea Council says Mr Prescott's department used his influence to try to persuade the town to withdraw its bid for a super casino licence to help the Dome's chances.
Mr Prescott dismissed the claims, saying: "I was not involved in it, did not even know about it until I read in the press, totally reject any idea that I expressed any pressure whatsoever."
Decisions on the super casino licence would be taken by Parliament once an independent commission gave its recommendation, he said.
Mr Prescott praised Mr Anschutz for his work at the Dome in turning a polluted plot of land into 24,000 homes and 10,000 jobs.
Liberal Democrat culture spokesman Don Foster said Mr Prescott cannot have been in charge of his departments if he had nothing to do with his officials talks about casinos.
Mr Foster said Mr Prescott was now "well past his sell-by date".