President Obama (L) with Mitt Romney at the event
US President Barack Obama and Republican rival, Mitt Romney have made a series of lighthearted jabs at themselves and each other at a charity fundraiser in New York.
At a benefit organised by the Catholic Archdiocese of New York Obama mocked his first debate performance while Romney poked fun at his own wealth, reports the BBC.
Earlier, Obama made an appearance on the Daily Show with Jon Stewart.
He said the US would "fix" security overseas after a deadly Libya attack.
Stewart asked Obama about the administration's "confused" response to the attack on a US consulate in Benghazi, Libya on September 11.
The US ambassador to Libya and three other Americans died in the attack, which remains at the centre of the campaign debate ahead of a foreign policy debate in Florida on Monday.
Obama told Stewart his administration was still piecing together the evidence.
"The government is a big operation. At any given time, something screws up and you make sure you find out what's broken and you fix it," he said.
Obama also repeated his wish to close the prison at Guantanamo Bay naval base in Cuba, a first term promise he has been criticised for not yet carrying out.
The Alfred F Smith Memorial Foundation Dinner - a traditional fixture on the presidential campaign calendar - was Romney's only public event on Thursday after several campaign stops in Virginia the day before.
On stage, Romney gently mocked his own Mormon faith, saying he had prepared for the presidential debates by "not drinking alcohol for 65 years".
Resplendent in formal white tie, Romney - known for his business fortune - said that after a long campaign it was "nice finally to relax and wear what Ann and I wear around the house".
And in a reference to the need to raise a laugh from among the attendees, he reminded the audience of the vice-president's mirth-filled approach to his debate with Paul Ryan a week ago: "I was hoping the president would bring Joe Biden along because he'll laugh at anything."
Obama used the occasion to reference the first debate between the two men, an encounter he was widely judged to have lost.
"I had more energy in second debate," the president said. "I was well-rested after the nice long nap I had in first debate."
Obama also noted he had been criticised for being too popular abroad at the beginning of his term. "I'm impressed with how well Governor Romney has avoided that problem," he said, in a nod to a summer overseas trip that drew criticism.
The dinner was overseen by Cardinal Timothy Dolan, the president of the US Conference of Catholic Bishops, which has clashed with the administration over contraception provisions in Obama's health care law.
Cardinal Dolan has said he received "stacks of mail" protesting against Obama's invitation to the dinner, but he sought to avoid playing political favourites. The cardinal delivered benedictions at both the Republican and Democratic national conventions in 2012.
Ahead of his reunion with Obama, a daily Gallup tracking poll of likely voters suggested Romney had increased his lead nationally. However, a series of other polls show a much tighter race.
Romney announced on Thursday that his campaign was leaving North Carolina, believing his victory was assured there. He is currently polling an average of six points ahead of Obama in the state.
Obama also benefited from new polling on Thursday, with a Pew Hispanic Center poll suggesting three-quarters of Catholic Latinos back the president.
The president picked up the backing of rock star Bruce Springsteen, as he did in 2008. Springsteen campaigned for Obama on Thursday in Ohio with former President Bill Clinton.