Obama and Romney swap jokes at Al Smith dinner

At the event organised by the Catholic Archdiocese of New York, Mr Obama said his first debate performance - which he was judged to have lost - had been a "long nap" to prepare for the second.

Mr Romney mocked his own wealth.

Referring to his Mormon faith. he said he had prepared for the debates by "not drinking alcohol for 65 years".

Earlier, Mr 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 Mr Obama about the administration's "confused" response to the attack on a US consulate in Benghazi, Libya on 11 September.

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.

Mr 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.

Mr 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.

Relax in a tie

The Alfred F Smith Memorial Foundation Dinner - a traditional fixture on the presidential campaign calendar - was Mr Romney's only public event on Thursday after several campaign stops in Virginia the day before.

Resplendent in formal white tie on stage, Mr 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."

Referring to the first presidential debate, Mr Obama said: "I had more energy in second debate. I was well-rested after the nice long nap I had in first debate."

Mr 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.

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