Washington (CNN) Vice President Joe Biden offered an account Tuesday of the decision to launch the raid that killed Osama bin Laden that differed from some of his previous retellings -- and from Hillary Clinton's.

His remarks come as he considers facing off against the former secretary of state in the 2016 presidential race, and they seem to signal that he sees his earlier stance on the raid as a potential liability.

At an event honoring former Vice President Walter Mondale, Biden said he had privately advised the President to pursue the raid on bin Laden's compound after initially advising a more cautious approach at a Cabinet meeting.

Pakistani media and residents gather outside the bin Laden hideout on May 3, 2011.

Pakistani media and residents gather outside the bin Laden hideout on May 3, 2011.

A visitor photographs the fence overlooking the crash site of Flight 93 in Shanksville, Pennsylvania, on May 2, 2011.

A visitor photographs the fence overlooking the crash site of Flight 93 in Shanksville, Pennsylvania, on May 2, 2011.

Danielle LeMack, left, Carie LeMack and Christie Coombs, who lost relatives on 9/11, pause during a ceremony to honor the victims on May 2, 2011, at the Garden of Remembrance in Boston.

Danielle LeMack, left, Carie LeMack and Christie Coombs, who lost relatives on 9/11, pause during a ceremony to honor the victims on May 2, 2011, at the Garden of Remembrance in Boston.

A passer-by looks at newspaper headlines in front of the Newseum in Washington.

A passer-by looks at newspaper headlines in front of the Newseum in Washington.

Students gather to celebrate at the fence on the north side of the White House.

Students gather to celebrate at the fence on the north side of the White House.

U.S. Marines watch the announcement of bin Laden's death at Camp Dwyer in Helmand Province, Afghanistan.

U.S. Marines watch the announcement of bin Laden's death at Camp Dwyer in Helmand Province, Afghanistan.

Revelers gather at the fence on the north side of the White House.

Revelers gather at the fence on the north side of the White House.

Crowds celebrate with NYPD officers in New York's Times Square early on May 2, 2011, after the death of Osama bin Laden.

Crowds celebrate with NYPD officers in New York's Times Square early on May 2, 2011, after the death of Osama bin Laden.

Servicemen cheer from a lamp post as thousands of people gather at Ground Zero in New York City.

Servicemen cheer from a lamp post as thousands of people gather at Ground Zero in New York City.

Vice President Joe Biden, left, President Barack Obama, and Secretary of State Hillary Clinton, second from right, watch the mission to capture Osama bin Laden from the Situation Room in the White House on May 1, 2011. Click through to see reactions from around the world following the death of the al Qaeda leader.

Vice President Joe Biden, left, President Barack Obama, and Secretary of State Hillary Clinton, second from right, watch the mission to capture Osama bin Laden from the Situation Room in the White House on May 1, 2011. Click through to see reactions from around the world following the death of the al Qaeda leader.

"We walked out of the room and walked upstairs," Biden said. "I told him my opinion: I thought he should go, but to follow his own instincts."

The new account is a significant departure from what he said at a Democratic retreat in January 2012.

"Mr. President, my suggestion is, 'Don't go,'" Biden said, according to an ABC News report from that time.

"'We have to do two more things to see if he's there,'" Biden recalled, though the story did not include what those two things were.

The Cabinet meeting Biden referred to has been described by several people in the administration, including President Barack Obama himself.

The President asked his closest advisers for input on how he should respond to intelligence that bin Laden was holed up in a compound in Abbottabad, Pakistan -- intelligence that was anything but certain.

The proposed raid by Navy SEALS was risky, particularly without notifying Pakistan of the plan.

"Those decisions are not always popular. Those decisions generally are not poll-tested," Obama told moderator Bob Schieffer in a 2012 presidential debate. "And even some in my own party, including my current vice president, had the same critique" about the risk of the operation as did some outsiders.

Clinton has also characterized Biden has having been openly skeptical in the meeting.

Photos: Photos: Vice President Joe Biden Photos: Photos: Vice President Joe Biden U.S. Vice President Joe Biden began his career in politics in 1972, winning election to the Senate at the age of 29 (he was 30 when he took office). The Delaware Democrat was reelected to the Senate six times, including 2008, before becoming the 47th vice president of the United States. Hide Caption 1 of 14 Photos: Photos: Vice President Joe Biden Biden is sworn in for his second term as vice president by Supreme Court Justice Sonia Sotomayor, with his wife, Jill, and son, Beau, by his side, on January 21, 2013, in Washington. Hide Caption 2 of 14 Photos: Photos: Vice President Joe Biden Biden presides over a ceremony in Baghdad to formally mark the end of the U.S. combat mission in Iraq on September 1, 2010. Hide Caption 3 of 14 Photos: Photos: Vice President Joe Biden Biden and President-elect Barack Obama wave to the crowd at their election night party at Grant Park in Chicago on November 4, 2008. Hide Caption 4 of 14 Photos: Photos: Vice President Joe Biden Biden speaks after being introduced as Obama's running mate while campaigning together after the Democratic National Convention in 2008. Hide Caption 5 of 14 Photos: Photos: Vice President Joe Biden From left, former Sen. John Edwards, Biden, Obama and Sen. Hillary Clinton at a debate of Democratic presidential candidates on April 26, 2007, in Orangeburg, South Carolina. Hide Caption 6 of 14 Photos: Photos: Vice President Joe Biden Biden releases his memoir, "Promises to Keep: On Life and Politics," in 2007. Hide Caption 7 of 14 Photos: Photos: Vice President Joe Biden As a ranking member of the Senate Foreign Relations Committee, Biden is interviewed on NBC's "Meet the Press," concerning the war in Iraq on August 14, 2005. Hide Caption 8 of 14 Photos: Photos: Vice President Joe Biden While chairman of the Senate Foreign Relations Committee, Biden meets Afghan students during a visit to Kabul in 2002. Hide Caption 9 of 14 Photos: Photos: Vice President Joe Biden Biden is welcomed back after undergoing surgery for an aneurysm in 1988. Hide Caption 10 of 14 Photos: Photos: Vice President Joe Biden Biden announces his candidacy for the Democratic presidential nomination in 1988. After three months he drops out, following reports of plagiarism and false claims about his academic record. Hide Caption 11 of 14 Photos: Photos: Vice President Joe Biden While on the Senate Judiciary Committee, Biden meets with Sen. Frank Church, center, and Egyptian President Anwar Sadat after the signing of the Egyptian-Israeli Peace Treaty in 1979. Hide Caption 12 of 14 Photos: Photos: Vice President Joe Biden President Jimmy Carter and Biden attend a reception for the Delaware Democratic Party in 1978. Biden was the first senator to endorse Carter's presidential candidacy two years earlier. Hide Caption 13 of 14 Photos: Photos: Vice President Joe Biden At a convention in 1972, Biden and his first wife, Neilia, and his two sons take a photo with Delaware Gov.-elect Sherman W. Tribbitt and his wife Jeanne. Neilia Biden died in a car accident a few months later, after his first election to the Senate, along with their infant daughter, Naomi. Hide Caption 14 of 14

Tuesday's account is also a change from an account Biden gave on NBC's "Meet the Press" in May 2012, in which he described advising the President to follow his instincts but didn't explicitly advise him to "go" for it.

"We walked up toward the residence, toward his office," said Biden of his conversation with Obama, "and I knew he was going to go (for the raid). And what I always tell him when he -- he looked at me again, and I said, 'Follow your instincts, Mr. President. Your instincts have been close to unerring; follow your instincts.'"

Biden also offered a reason for the difference between what he said in the Cabinet meeting and his new account of the private conversation with Obama in which he advocated following his instincts.

The vice president now says that he suggested the administration undertake additional drone surveillance on the compound while in that Cabinet meeting, but that he made that recommendation because he didn't want to undermine the President if he ended up choosing a more cautious approach.

"Imagine if I had said, in front of everyone, don't go or go and his decision was a different decision," said Biden. "It undercuts that relationship. So I never, on a difficult issue, never say what I think finally until I go up to the Oval with him alone."

Biden also said Tuesday that only two people in the meeting were definitive in their advice to the President, contradicting Clinton's account of how she supported the mission.

There were "only two people who were definitive and were absolutely certain," he said, referring to the men who were, respectively, the director of the CIA and the secretary of defense at the time. "Leon Panetta said, 'Go,' and Bob Gates -- who has already publicly said this -- said, 'Don't go.' And others were at 59/41."

In her 2014 book "Hard Choices," Clinton writes that she was an immediate supporter while Biden "remained skeptical."

"I respected Bob [Gates] and Joe [Biden]'s concerns about the risks of a raid, but I came to the conclusion that the intelligence was convincing and the risks were outweighed by the benefits of success," she wrote. "We just had to make sure it worked."

Biden also drew attention in his remarks Tuesday to the fact that he knew about the intelligence on bin Laden's location before Clinton did.

"The President and I, and only two others in the administration, knew about Abbottabad as early as August" 2010, Biden said Tuesday. "We did not go for almost a year to get him. And major players in the Cabinet did not know about it till January or February (2011)."

In Clinton's account, she learned about the intelligence in March 2011.