The Republican presidential nominee, who spoke first, told the Alfred E. Smith Memorial Foundation Dinner, "It's nice to finally relax and wear what Ann and I wear around the house."
He said he and Obama, who sat with New York Cardinal Timothy M. Dolan at the Thursday dinner, "were chatting pleasantly this evening as if Tuesday night never happened," referring to their heated presidential debate that at times appeared like a spoken-word mixed martial arts match, with both candidates verbally striking and grappling.
Romney said he was happy to be at the Catholic charity fundraiser that attracts top New York luminaries from politics, the media and finance, but he imagined the media would be unfair to him: "The headlines will be: 'Obama embraced by Catholics, Romney dines with rich people.'"
He noted New York Gov. Andrew Cuomo was at the dinner and is known as a man with presidential ambitions.
"Governor Cuomo may be getting ahead of himself," Romney said. "He has put in one term as governor, he has a father who was governor and he thinks that is enough to run for president!"
Romney noted his remarks were supposed to be funny.
"I was actually hoping the president would bring Joe Biden along, because he'll laugh at anything," Romney said.
Referring to the first presidential debate Oct. 3 and his comment about Big Bird from the PBS children's TV show "Sesame Street," Romney told the audience Obama's remarks would be "brought to you by the letter O and the number 16 trillion," a reference to the national debt.
He also said that as someone who's running for the White House, "It's good to have someone you can depend on at the end of the day. I have my wife, Ann. President Obama has Bill Clinton."
When Obama stepped to the lectern, he asked the audience to "please take your seats -- otherwise, Clint Eastwood will yell at them," referring to the actor's speech to an empty chair at the Republican National Convention.
He said he was much more energetic during Tuesday's presidential debate than in the first one because "I felt really well rested after the nice long nap I had in the first debate."
He added, "I learned that there are worse things that can happen to you on your anniversary than forgetting to buy a gift."
Obama offered his own Biden joke, saying: "I've heard some people say, 'Barack, you're not as young as you used to be. Where's that golden smile? Where's that pep in your step?'
"And I say, 'Settle down, Joe. I'm trying to run a Cabinet meeting here.'"
Obama noted Mitt is actually Romney's middle name. "I wish I could use my middle name," said Obama, whose middle name is Hussein. Romney's first name is Willard.
"The unemployment rate is at its lowest level since I took office," Obama said, pausing a moment, then adding: "I don't have a joke here. I just thought it would be useful to remind everybody."
He also reminded everybody that Monday's debate would focus on foreign policy. "Spoiler alert," he said. "We got bin Laden."
Master of ceremonies Al Smith IV noted his great-grandfather was the first Catholic nominee for president, and Romney is the first Mormon. He added they have other things in common. "They both campaigned for governor -- as Democrats."
"Also, their biggest adversaries were successful businessmen. For my great-grandfather it was Herbert Hoover. For Mitt Romney, it was Mitt Romney."
He said Romney is a very wealthy man, and a generous man. "Every year he gives at least 10 percent of his income to charity. [Applause] Not so fast! The charity is the federal government."
He said the archdiocese didn't invite Romney to the dinner to speak -- "we invited him here to convert," adding: "Really, governor, your father was from Mexico and you have five kids. Are you sure you're not Catholic?"
To Obama, Smith said: "You're not getting a free pass tonight. We're excited to have you here tonight -- almost as excited as we were in 2008."
Smith said the church owed Obama a debt of gratitude for illuminating a teaching of Jesus.
"Jesus taught us that it's easier for a camel to pass through the eye of a needle than it is for a rich man to enter the kingdom of heaven. Say what you will about the economy, Mr. President, it's going to be a lot easier for a lot more people to get into heaven," Smith said.
He also said he recognized Obama has challenges this year. "It's never good when your opponent has produced more sons than you produced jobs. I'm pretty sure that number's accurate. [Romney running mate] Paul Ryan gave it to me."