NEW YORK (AP) — Republican White House hopeful Mitt Romney is unlikely to win Bill Clinton's vote, but that doesn't mean he can't soak up a bit of the popular former president's luster.

The two men stood side by side Tuesday as Clinton introduced Romney before the GOP candidate's speech to Clinton's annual global conference in New York. Clinton recalled working with Romney to save AmeriCorps, and praised the former Massachusetts governor's efforts to persuade fellow Republicans to support the national service program.

Romney, taking the podium, returned the compliment.

"If there's one thing we've learned in this election season, by the way, it is that a few words from Bill Clinton can do a man a lot of good," he said, prompting loud laughter and applause from the crowd.

It was a clear nod to Clinton's speech praising President Barack Obama at the Democratic National Convention in Charlotte, N.C., earlier this month, and the slight uptick in the polls that Obama enjoyed soon after.

"All I got to do now is wait a few days for that bounce to happen," Romney quipped.

Such moments of bipartisan levity have been rare in a campaign marked by harsh accusations, heavy-handed rhetoric and relentless attack ads between the presidential campaigns and the outside groups that support them.

Obama's campaign currently is running one such ad against Romney that uses a clip of Clinton's convention speech where the former president says Romney wants to "take us back to the policies that got us into trouble in the first place."

But any resentment was noticeably absent Tuesday as Clinton and Romney appeared chummy, patting each other on the shoulder and chatting onstage after Romney's speech.

"That was good," Clinton told the man hoping to dislodge Clinton's party from the White House.

Before the speech, Romney spoke backstage with Clinton and Clinton's daughter, Chelsea, said Romney spokesman Rick Gorka. He declined to say what they discussed.

Clinton has an outsized influence on the presidential election more than a decade after he left office. Both Obama and Romney have pointed to Clinton's economic leadership as an example for the nation, citing prosperity and a federal budget that was balanced under his leadership.

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Clinton is using the full weight of those credentials to boost Obama's bid. In his convention speech, he systematically rebutted Romney's attacks on Obama, accusing the Republican of pushing an economic plan that doesn't add up.

The Obama-Clinton political alliance was back on display a few hours later when the two Democrats shared a handshake and a hug on the same stage where Romney had spoken earlier in the day.

Normal protocol, Clinton said, would require him to simply introduce the president and then be quiet.

"I just want to make one comment. I'm going to finish that speech I started in Charlotte," he said, poking fun at himself over a sermon that at times seemed like it might never end.

Obama, before beginning a wrenching speech about human trafficking, thanked Clinton for the warm introduction.

"Although I have to admit," Obama joked, "I really did like the speech a few weeks ago a little bit better."

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Lederman reported from Washington. AP White House Correspondent Ben Feller in New York contributed to this report.