Two days after a televised debate in which they exchanged verbal blows and stalked each other on stage, Mr Obama and Mr Romney greeted each other warmly, dressed formally in white tie and tails.

But the combativeness of the campaign trail was ever-present as the two foes gave back-to-back speeches at the 67th annual Alfred E. Smith Memorial Foundation Dinner.

Mr Romney said Mr Obama, who wants to increase taxes on the wealthy to help fund government programmes, must have had some thoughts as he looked out at the crowd of wealthy people.

"You have to wonder what he's thinking: so little time, so much to redistribute," he said.

Mr Obama made fun of Mr Romney's vast wealth.

"Earlier I went shopping at some stores in Midtown. I understand Governor Romney went shopping for some stores in Midtown," he said.

The event was a glittering affair at the famous Waldorf Astoria Hotel where New York's high society dined on poached lobster and rack of lamb and contributed $5million for various children's charities.

Mr Obama and Mr Romney face a final debate on Monday in Florida