LAS VEGAS (AP) – President George W Bush said yesterday the trio of prime-time debates with Senator John Kerry demonstrated he is running on his record – and his opponent away from his own – even as the Republican campaign acknowledged that Kerry had gained from the confrontations viewed by tens of millions of Americans.

“The senator’s record is 20 years of out-of-the-mainstream votes without any significant reforms or results,” Bush told thousands of cheering supporters amid post-debate polls showing Kerry was widely viewed as winning each one. “I’m proud of my record. My opponent seemed to want to avoid talking about his.”

Marc Racicot, Bush’s campaign chairman, insisted that any advantage to Kerry from the debates would prove fleeting.

Assessing all the debates combined, Racicot said Kerry “did provide himself some temporary assistance with the first debate that got more leavened in the second debate and then began to dissipate at a whatever unknown rate with last night’s performance. I just think he was on his heels most of the night.”

Bush and Kerry set out on an 19-day campaign sprint to the November 2 election, concentrating their time and advertising on a dozen or so key states that will settle it. The ubiquitous polls made their race a virtual dead heat.

The Democratic Party was quick to publicise what it called a debate “threepeat” for Kerry, launching two videos that mocked Bush’s performance. One shows Bush talking about Osama bin Laden and telling White House reporters, “I truly am not that concerned about him. I know he is on the run,” then denying during the debate that he had ever said it.

The other video shows Bush laughing when asked about uninsured Americans.

Bush played down negative reviews of his debate performances. “The pundits and the spinners – they all have their opinions but there’s only one opinion that matters and that’s the opinion of the American people on November 2,” he told reporters during a rare visit to the press cabin on the presidential plane, Air Force One. “I feel great about where we are.”

“My spirits are high,” Bush declared. “I’m enthusiastic about my chances.”

Kerry’s day included an appearance before the AARP’s national convention in Las Vegas. The organisation of Americans 50 and older lent crucial support to controversial Medicare prescription drug legislation that Bush won from Congress a year ago. Kerry opposed the measure and polls now show support for it lags among older Americans.

Bush decided to skip the convention and first lady Laura Bush was taking his place. The president headed instead to a rally with Republican governors, also meeting in Las Vegas.

For undecided voters, Wednesday night’s debate was a chance to comparison-shop. Kerry cast himself as champion of the little guy and Bush the guardian of the wealthy, branding the president as reckless with the federal budget and the use of American force. Bush labeled Kerry a do-nothing liberal senator with questionable credibility and an insatiable appetite for taxes. A question about federal spending and deficits yielded one of their sharpest exchanges.

“You know, there’s a mainstream in American politics, and you sit right on the far left bank,” Bush said, charging that Kerry had voted to exceed budget ceilings 277 times.

“Being lectured by the president on fiscal responsibility is a little bit like Tony Soprano talking to me about law and order in this country,” Kerry said, referring to the Mafia boss character on the television show “The Sopranos.” “This president has taken a $5.6 trillion (euro4.5 trillion) surplus and turned it into deficits as far as the eye can see.”

Both candidates said they believe marriage should remain a union of a man and a woman but that gay Americans should be treated with respect. Kerry cited Mary Cheney, the vice president’s openly gay daughter and an official in the campaign, as a lesbian who probably would say being gay is not a matter of choice.

That drew a rebuke from both Dick Cheney and his wife, Lynne. In a veiled reference to Kerry’s remarks about his daughter, the vice president told supporters in Florida yesterday, “You saw a man who will do and say anything to get elected, and I am not just speaking as a father here, although I am a pretty angry father.”

Earlier, Mrs Cheney called Kerry “not a good man” and described his remarks as “a cheap and tawdry political trick.”

Kerry responded yesterday: “I love my daughters. They love their daughter. I was trying to say something positive about the way strong families deal with this issue.”

In an interview yesterday with ABC Radio, Elizabeth Edwards, wife of Democratic vice presidential candidate John Edwards, said Mrs Cheney “overreacted to this and treated it as if it’s shameful to have this discussion.”

Bush seemed to find his stride after two debates that most viewers and analysts thought he lost. He stifled most of the facial expressions that marred his first performance, ending each answer with a smile, though the camera occasionally captured him dropping it abruptly a few seconds later. After letting his voice rise to a shout during the second debate, Bush toned it down, speaking more softly.

Kerry was seen as the winner in two of three post-debate polls, while the third found the two tied.