A day after a muted performance in a presidential debate, US President Barack Obama fought back against Republican rival Mitt Romney on Thursday and the Democrat's re-election campaign vowed to learn lessons from the setback.

A feisty Obama told a rally of some 12,000 people that the former Massachusetts governor was untruthful during Wednesday's 90-minute debate in Denver, which most observers reckoned the Republican won.

"When I got onto the stage, I met this very spirited fellow who claimed to be Mitt Romney," Obama said.

"But it couldn't have been Mitt Romney, because the real Mitt Romney has been running around the country for the last year promising $5 trillion in tax cuts that favor the wealthy. The fellow on stage last night said he didn't know anything about that."

Often criticized for being wooden, Romney's aggressive debate performance gave his campaign a burst of energy after weeks of setbacks.

Looking at times tired and displeased, Obama did not seize opportunities to attack the Republican on his business record at Bain Capital, the "47 percent" video and his refusal to release more income tax returns.

All this unfolded before a national television audience of 67.2 million, according to television ratings firm Nielsen, up 28 percent compared wit the first presidential debate in 2008 between Obama and Republican Senator John McCain.

With two more presidential debates before the Nov. 6 election, senior aide David Axelrod said the Obama campaign would adjust its strategy as a result of the debate.

"We are going to take a hard look at this and we are going to have to make some adjustments as to where to draw the lines in these debates and how to use our time," he told reporters.

Democratic sources said Obama raised more than $100 million in September in another sign of his financial strength going into the last month of the campaign.

Romney prepared for the Denver encounter with days of mock debates and was more ready to go on the offensive against Obama in detailed discussion on taxes, jobs, energy and the budget deficit.

Obama is unlikely to add "huge amounts of additional prep time," for the two other debates, on Oct. 16 in New York and on Oct. 22 in Florida, Axelrod said.

Part of the Obama strategy will be to attack Romney for what the Democratic campaign says are untruthful statements during the debate on his tax plan, Medicare and deficit cutting, as well as pressing him on what appeared to be changes in position on issues like bank regulation.

"We obviously are going to have to adjust for the fact of Mitt Romney's dishonesty," senior advisor David Plouffe said. "It's hard to remember a time in American politics when you have someone who is a major nominee for the presidency being that fundamentally dishonest about core parts of his campaign platform."

Obama spoke to a large crowd in Madison, Wisconsin, on Thursday afternoon that his campaign said was 30,000 strong.

ROMNEY SWAGGER, POLL BOOST

Romney had a bounce in his step and confidence in his voice as he addressed more than 10,000 supporters in Fishersville, Virginia, in the Shenandoah Valley.

In a sign of the importance of the state for him, Romney appeared together with his vice presidential nominee, Paul Ryan.

Romney, appearing after country singer Trace Adkins energized the crowd, said the debate offered two different visions for the country.

"What you didn't hear last night from the president is why it is the next four years are possibly going to be better than the last four years. He doesn't have a way to explain that, because he has the same policies for the next four years as he had for the last four years," Romney said.

The debate win was badly needed by Romney, whose poll numbers had dropped in recent weeks after several missteps and the release of a damaging video showed him disparaging 47 percent of the electorate as dependent on government aid.

Going into the debate, Obama held a lead of 5 to 6 percentage points over Romney in most national polls, and is ahead by at least narrow margins in almost all the battleground states where the election will be decided.

But Romney is now viewed positively by 51 percent of voters, the first time he has enjoyed a net positive in the presidential race, according to a Reuters/Ipsos poll taken after the debate. Obama's favorability rating remained unchanged at 56 percent. – Reuters