"I'd be lying if I said that I knew I was there," Biden, whose son Beau died recently, said in the interview. "Nobody has a right, in my view, to seek that office unless they're willing to give it 110 percent of who they are."
Colbert urged the vice president to run.
"I think your experience and your example of suffering and service is something that would be sorely missed in the race," said the comedian, who suffered tragedy himself as a child when his father and two of his brothers died in a plane crash.
See pics of Joe Biden throughout the years:
Joe Biden through the years
Emotional Biden says not 'there' when asked about presidential run
Democratic politician Joseph R. Biden Jr, the United States Senator from Delaware, circa 1980. He became the US Vice President in 2009 under President Barack Obama. (Photo by Nancy Shia/Archive Photos/Getty Images)
WASHINGTON, : US Senator Joe Biden(D-DE) briefs reporters prior to the 15 January start of the second day of the US Senate impeachment trial of US President Bill Clinton on Capitol Hill in Washington, DC. House prosecutors will summarize their case against the president 15 January. (ELECTRONIC IMAGE) AFP PHOTO/Luke FRAZZA (Photo credit should read LUKE FRAZZA/AFP/Getty Images)
392389 02: U.S. President George W. Bush meets with members of the Senate and House foreign policy leadership in the Cabinet room at the White House July 25, 2001 in Washington, DC. Seated next to the president is Sen. Joe Biden (D-DE). (Photo by Mark Wilson/Getty Images)
UNITED STATES - MARCH 08: Joe Biden during the 2004 Democratic National Convention in Boston, Massachusetts. (Photo By Douglas Graham/Roll Call/Getty Images)
UNITED STATES - MAY 12: Democrat vice chairman of the Senate Foreign Relations Committee Senator Joe Biden (D-DE), throws up his hands as he speaks during debate on the nomination of John Bolton as US Ambassador the the United Nations May 12, 2005 in Washington D.C. (Photo by Joe Marquette/Bloomberg via Getty Images)
WASHINGTON - JULY 12: U.S. Senator Joseph Biden (D-DE) speaks during the Senate Foreign Relations Committee hearing on 'North American Cooperation on the Border' on the Border' on Capitol Hill July 12, 2005 in Washington, DC. The committee discussed border security and how to work together to secure the borders with Mexico and Canada. (Photo by Joe Raedle/Getty Images)
THE TONIGHT SHOW WITH JAY LENO -- Episode 3331 -- Pictured: (l-r) Senator Joe Biden during an interview with host Jay Leno on March 22, 2007 (Photo by Paul Drinkwater/NBC/NBCU Photo Bank via Getty Images)
ORANGEBURG, SC - APRIL 26: (L-R) U.S. Sen. Joe Biden (D-DE) and New Mexico Gov. Bill Richardson greet the crowd before the start of the first debate of the 2008 presidential campaign April 26, 2007 at South Carolina State University in Orangeburg, South Carolina. The debate, featuring eight Democratic presidential candidates, comes 263 days before the first ballot will be cast in the Iowa caucus next January. (Photo by Justin Sullivan/Getty Images)
WASHINGTON, DC - JANUARY 23: U.S. Vice President Joe Biden (C) talks with mayors from across the country, including Milwaukee Mayor Tom Barrett, in the Roosevelt Room of teh White January 23, 2014 in Washington, DC. The U.S. Conference of Mayors is holding its annual conference in Washington this week. (Photo by Chip Somodevilla/Getty Images)
US Vice President Joe Biden speaks during the Civil Society Forum on the sideline of the US-Africa Leaders Summit in Washington, DC, on August 4, 2014. Washington aims to wake up US business to the opportunities in Africa with the landmark US-Africa Leaders Summit this week, as China and Europe steal a march on the world's fastest-growing continent. As many as four dozen African leaders, and hundreds of businessmen with them, will for their part be looking to see if US investors and traders can move beyond old stereotypes of a continent mired in conflict and corruption and recognize its huge potential. AFP PHOTO/Jewel Samad (Photo credit should read JEWEL SAMAD/AFP/Getty Images)
WASHINGTON, DC - AUGUST 18: U.S. Vice President Joe Biden (R) swears in Secretary of Housing and Urban Development Julian Castro (L) as his wife Erica and daughter Carina look on during a ceremonial swearing in ceremony in the Eisenhower Executive Office Building August 18, 2014 in Washington, DC. Castro, the former Mayor of San Antonio, Texas, was officially sworn in on July 28. (Photo by Win McNamee/Getty Images)
WASHINGTON, DC - JUNE 30: (AFP OUT) U.S. President Barack Obama (C), Robert McDonald (R) and Vice President Joe Biden walk back to the White House through LaFayette Park after President Obama announced his intention to nominate Robert McDonald to lead the Department of Veterans Affairs June 30, 2014 in Washington, DC. McDonald served as the chief executive of Procter & Gamble and will replace Eric Shinseki who resigned after allegations of delayed care came to light. (Photo by Dennis Brack-Pool/Getty Images)
US President Barack Obama speaks to US Vice President Joe Biden after Biden introduced him during a signing ceremony for H.R. 803, the Workforce Innovation and Opportunity Act, on July 22, 2014 in the South Court Auditorium of the Eisenhower Executive Office Building, next to the White House in Washington, DC. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images)
US Presidential Barack Obama speaks on immigration reform beside US Vice President Joe Biden (R) in the Rose Garden of the White House on June 30, 2014 in Washington, DC. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images)
COLORADO SPRINGS, CO - MAY 28: Vice President of the United States Joe Biden takes a selfie after the commencement ceremony at Air Force Academy in Colorado Spring, May 28, 2014. Biden spoke during the ceremony. (Photo by RJ Sangosti/The Denver Post via Getty Images)
US Vice President Joe Biden gestures as he speaks at Ledra palace in the UN-patrolled Buffer Zone in Nicosia on May 22, 2014. Biden met Cyprus leaders Thursday to spur talks on ending the island's 40-year division and seek support for threatened sanctions against Russia despite the economic cost. AFP PHOTO/ ANDREW CABALLERO-REYNOLDS (Photo credit should read Andrew Caballero-Reynolds/AFP/Getty Images)
US Vice President Joe Biden adresses a speech to students and officials at Cotroceni Palace, the Romanian Presidency headquarters in Bucharest on May 21, 2014. Tougher sanctions must be imposed on Russia if it undermines crucial presidential elections in Ukraine on May 25, 2014, US Vice President Joe Biden said in Bucharest. AFP PHOTO DANIEL MIHAILESCU (Photo credit should read DANIEL MIHAILESCU/AFP/Getty Images)
WASHINGTON, DC - APRIL 29: U.S Vice President Joe Biden speaks during an event on protecting students from sexual assault at the Eisenhower Executive Office Building April 29, 2014 in Washington, DC. During the event, Biden announced the release of the first report of the White House Task Force to Protect Students from Sexual Assault. (Photo by Win McNamee/Getty Images)
US Vice President Joe Biden (L) and outgoing Heath and Human Services Secretary Kathleen Sebelius applaud as President Barack Obama names Sylvia Mathews Burwell (R), his current budget director, to replace Sebelius in the Rose Garden at the White House in Washington,DC on April 11, 2014. Sebelius resigned, paying the price for the chaotic initial rollout of the US president's signature health care law. AFP PHOTO/Nicholas KAMM (Photo credit should read NICHOLAS KAMM/AFP/Getty Images)
US Vice President Joe Biden waves upon arrival for a meeting with Lithuania's President in Vilnius on March 19, 2014. Biden meets today with Lithuanian President Dalia Grybauskaite and Latvian leader as part of a tour to reassure NATO allies during the Ukraine crisis. AFP PHOTO / PETRAS MALUKAS (Photo credit should read PETRAS MALUKAS/AFP/Getty Images)
US Vice President Joe Biden listens during a meeting with the Polish Prime Minister in Warsaw, Poland on March 18, 2013. Biden arrived in Poland for talks with regional allies as Russia tightened its grip on the Ukraine's breakaway region of Crimea. AFP PHOTO / JANEK SKARZYNSKI (Photo credit should read JANEK SKARZYNSKI/AFP/Getty Images)
US Vice President Joe Biden arrives for a St. Patrick's Day reception in the East Room of the White House on March 14, 2014 in Washington. AFP PHOTO/Mandel NGAN (Photo credit should read MANDEL NGAN/AFP/Getty Images)
US Vice President Joe Biden during a joint press conference with Chile's President Sebastian Pinera (not framed) at La Moneda presidential palace in Santiago, on March 10, 2014. AFP PHOTO/CLAUDIO REYES (Photo credit should read Claudio Reyes/AFP/Getty Images)
WASHINGTON, DC - FEBRUARY 27: U.S. Vice President Joe Biden delivers remarks during the Democratic National Committee's Winter Meeting at the Capitol Hilton February 27, 2014 in Washington, DC. Biden addressed the Association of State Democratic Chairs. (Photo by Chip Somodevilla/Getty Images)
THE VIEW - Joe Biden, the 47th Vice President of the United States, was the special guest, live, TUESDAY, FEBRUARY 25 (11:00 a.m.-12:00 noon, ET). The Vice President discussed the Affordable Care Act and the importance of signing up for health insurance through the marketplace before the March 31 deadline. Vice President Biden sat down with The View hosts Barbara Walters, Whoopi Goldberg, Sherri Shepherd and Jenny McCarthy as part of the shows continuing Red, White & View campaign, which is committed to political guests and discussions. 'The View' airs Monday-Friday (11:00 am-12:00 pm, ET) on the ABC Television Network.
(Photo by Lou Rocco/ABC via Getty Images)
SHERRI SHEPHERD, BARBARA WALTERS, VICE PRESIDENT JOE BIDEN, WHOOPI GOLDBERG, JENNY MCCARTHY
U.S. Vice President Joe Biden, left, looks on as President Barack Obama speaks at the White House in Washington, D.C., U.S., on Friday, Jan. 31, 2014. Obama is meeting today with chief executive officers of companies from Bank of America Corp. to EBay Inc. who have committed to giving the long-term unemployed a better chance in the hiring process. Photographer: Joshua Roberts/Bloomberg via Getty Images *** Barack Obama; Joe Biden
US Vice President Joe Biden gives two thumbs-up prior to US President Barack Obama delivering the State of the Union address before a joint session of Congress on January 28, 2014 at the US Capitol in Washington. AFP PHOTO/Saul LOEB (Photo credit should read SAUL LOEB/AFP/Getty Images)
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Positive poll numbers have led the former senator, who has twice before run for president, to consider joining the race to challenge former Secretary of State Hillary Clinton for the 2016 Democratic presidential nomination.
Clinton's front-runner status has eroded because of controversy over her use of a private email server while working in the Obama administration.
But the death of Beau Biden, who had urged his father to run, has left the vice president struggling to commit to a race.
Biden recalled a recent trip to Denver where he greeted military families and broke down when someone told him he had served with his son in Iraq.
"All of a sudden I lost it," Biden said, suggesting that was not something a presidential candidate should do. "That's not, I shouldn't be saying this: You can't do that."
Colbert set a serious tone for most of the interview, which took place during his first week hosting the show. A few glitches showed. Biden's microphone did not work at the beginning, so the taping was stopped to fix it.
The vice president, who is known for the occasional gaffe, joked he was used to having the White House shut off his mic too.