The campaign did not immediately respond to a request for details on Biden's claim.
It was a rare mention of foreign policy in a campaign that has been dominated by the economy. Polls show Obama leading Romney on who voters see as stronger on foreign policy issues, an uncommon advantage for Democrats on the issue.
Romney has said he would consider military action in Syria if the war-torn country's chemical weapons were at risk of falling into the wrong hands. Obama, who has opposed military action in Syria, has called it a "red line" for the U.S. if Syrian President Bashar Assad's regime were to use chemical or biological weapons.
And like Obama, Romney has said the U.S. must keep all options on the table, including a military strike, when dealing with Iran. But Romney has suggested that Obama has been too soft on Iran and without offering specifics said he would prevent Iran from obtaining a nuclear weapon.
Romney raised eyebrows when he failed to mention the Afghan war during his prime-time speech at the Republican Party's national convention last week.
Romney senior adviser Eric Fehrnstrom on Sunday defended the omission during an interview on CNN's "State of the Union." Ferhnstrom said Romney had already addressed the issue the day before in a speech to the American Legion.
"But Gov. Romney's convention speech was an opportunity for him to introduce himself to millions of voters who were seeing him for the first time," he said. "In that speech, he accomplished what he set (out) to do, which is to talk about his better vision for America, with more jobs and increasing wages. He talked about the failures of the Obama presidency over the last four years."
Obama's campaign plans to play up that strength during the Democrats' national convention, set to open Tuesday in Charlotte, N.C. Massachusetts Sen. John Kerry, a possible second-term secretary of state under Obama, will highlight the president's foreign policy record Thursday night before Obama formally accepts the Democratic nomination.
Obama himself trumpeted his foreign policy credentials Saturday during a rally in Des Moines, Iowa.
"I said we'd take out bin Laden and we did," said Obama, referencing the raid he ordered that led to the death of the al-Qaida leader.
Former New Mexico Gov. Bill Richardson, an Obama supporter, previewed some of Kerry's likely message on Sunday.
"The president has gotten us out of Iraq. We're getting out of Afghanistan," Richardson said on CBS' "Face the Nation." "We've got free trade agreements in Latin America we have a president that brilliantly dealt with the situation in Libya, with the Arab spring."
Thousands of delegates and volunteers were arriving in Charlotte during the Labor Day weekend ahead of the Democratic convention.
About 600 people marched Sunday through Charlotte's central business district to protest corporate greed in a demonstration that was lively but smaller than organizers had touted. The marchers carried signs and banners, banged drums and chanted on a sunny afternoon as part of the March on Wall Street South. Their numbers were a fraction of the 5,000 that organizers expected for what was likely to be the week's biggest protest.
Romney spent Sunday at his New Hampshire vacation home. He and his wife, Ann, attended church services Sunday morning at the chapel of the Church of Jesus Christ of Latter-Day Saints in Wolfeboro, N.H.
Campaign officials said Romney would spend much of the Democrats' convention week preparing for the presidential debates.
Obama was campaigning Sunday in Boulder, Colo., on the middle leg of a three-day battleground state trip in the lead-up to his convention.
Viewership was down markedly for the GOP convention this year. According to The Nielsen Co., some 30 million viewers tuned in Thursday night when Romney gave his acceptance speech, compared to some 40 million who watched Arizona Sen. John McCain accept the Republican nomination in 2008.
Democrats were eager to recapture the spotlight at their own gathering. But the convention's location served as an unwelcome reminder to the Democrats of an economy so weak that it threatens Obama's chances for re-election.
The president carried North Carolina in 2008, but the state's unemployment rate is pegged at 9.6 percent, higher than the nation's 8.3 percent and tied with next-door South Carolina for fifth from the bottom.
The Democrats' convention at the Time Warner Cable arena will feature evening speeches Tuesday by first lady Michelle Obama and San Antonio Mayor Julian Castro, the keynote speaker.
The president will be nominated for a new term on Wednesday, when former President Bill Clinton also will speak.
Obama's prime-time acceptance speech, to be delivered at the outdoor Bank of America Stadium, caps the convention on Thursday night. Aides predict a capacity crowd will hear the speech at the site, which can hold nearly 74,000. Vice President Joe Biden delivers his own acceptance speech the same evening.
Democrats are taking their turn in the convention spotlight just days after the Republicans met in Tampa to nominate Romney for the White House and Wisconsin Rep. Paul Ryan to be vice president.
Associated Press writers Beth Fouhy in Charlotte, N.C. and Kasie Hunt in Wolfeboro, N.H. contributed to this report.