WASHINGTON -- Sharply at odds over the Republican's assertions that he may not concede if he loses on Election Day, Donald Trump and Hillary Clinton chose cutting jabs over lighthearted teasing as they came face-to-face at a fundraiser. Yet both showed flashes of willingness to see beyond their bitter election battle, the archbishop who sat between them said Friday.

Still, New York's Cardinal Timothy Dolan summed up the two candidates' chemistry at a fundraiser in a word: "Awkward."

The controversy over Trump's remarkable assertions trailed the candidates to the Alfred E. Smith Memorial Foundation Dinner on Thursday, a traditionally genial event that turned bitter at times. Dolan, thrust into the role of temporary peacemaker, described a less antagonistic moment backstage after he invited them to pray.

"After the little prayer, Mr. Trump tuned to Secretary Clinton and said, 'You know, you are one tough and talented woman,' and he said this has been a good experience," Dolan told NBC's "Today" on Friday. "And she said, 'Donald, whatever happens, we need to work together afterwards."

The private moment at an annual Catholic fundraiser in New York was a rare departure from the unsympathetic tone both candidates have struck toward each other in a campaign that has been dominated by deeply personal, no-holds-barred attacks.

"We have proven we can actually be civil with each other," Trump said about the opponent he has asserted belongs in jail for alleged criminal acts. "In fact, just before taking the dais Hillary accidentally bumped into me and she very civilly said, 'Pardon me."'

Following Trump at the dinner, Clinton cracked: "I didn't think he'd be OK with a peaceful transition of power."

Republicans and Democrats alike have piled on Trump for refusing to say in the final debate whether he would concede if he loses. On Thursday, Trump said he would accept the results "if I win" or there was a clear outcome, but reserved his right to "contest or file a legal challenge" if he lost on Nov. 8.

He brushed off the likelihood of that happening, confident predicting that "we're not going to lose."

Among those criticizing Trump was Sen. John McCain, the Arizona Republican who lost to Barack Obama in the 2008 presidential race.

"I didn't like the outcome of the 2008 election. But I had a duty to concede, and I did so without reluctance," McCain said in a statement. "A concession isn't just an exercise in graciousness. It is an act of respect for the will of the American people, a respect that is every American leader's first responsibility."

While Trump maintained he would win, numerous Republican leaders conceded he was heading for defeat barring a significant shift in the campaign's closing days. The GOP's top concern was turning to salvaging its majority in the Senate, followed closely by worries over the Republicans' once comfortable grip on the House.

At the dinner, a tradition intended to bring candidates together in a display of national unity, Trump drew some boos and jeers in the Waldorf-Astoria ballroom when he referred to Clinton being "so corrupt" and said without apparent humour that she was appearing at the event "pretending not to hate Catholics" -- a line delivered during a benefit for the Roman Catholic Archdiocese of New York.

Clinton's jokes were cutting but delivered in the more accepted fashion of a roast. While several women have accused Trump of being sexually aggressive, Clinton steered clear of that controversy but referenced his public comments about the appearance of women: Donald looks at the Statue of Liberty and sees a 4 -- maybe a 5 if she loses the torch and tablet and changes her hair."

During an Ohio rally earlier Thursday, Trump tried to turn the attention to Clinton by accusing her of "cheating" and suggesting she should "resign from the race." He cited a hacked email disclosed publicly by WikiLeaks that showed her campaign was tipped off about a question she'd be asked in a CNN town hall meeting during the Democratic primary.

"Can you imagine if I got the questions? They would call for the re-establishment of the electric chair, do you agree?" Trump said.