The band's publicist, Heather Lylis, said Travers died Wednesday at Danbury Hospital in Connecticut.
Bandmate Peter Yarrow said that in her final months, Travers handled her declining health with bravery and generosity, showing her love to friends and family "with great dignity and without restraint."
"It was, as Mary always was, honest and completely authentic," he said. "That's the way she sang, too - honestly and with complete authenticity."
Noel "Paul" Stookey, the trio's other member, praised Travers for her inspiring activism, "especially in her defense of the defenseless."
"I am deadened and heartsick beyond words to consider a life without Mary Travers and honored beyond my wildest dreams to have shared her spirit and her career," he said.
Mary Allin Travers was born on Nov. 9, 1936, in Louisville, Kentucky, the daughter of journalists who moved the family to Manhattan's bohemian Greenwich Village. She quickly became enamored with folk performers like the Weavers and was soon performing with Pete Seeger, a founding member of the Weavers who lived in the same building as the Travers family.
With a group called the Song Swappers, Travers backed Seeger on one album and two shows at Carnegie Hall. She also appeared (as one of a group of folk singers) in a short-lived 1958 Broadway show called "The Next President," starring comedian Mort Sahl.
It wasn't until she met up with Yarrow and Stookey that Travers would taste success on her own. Yarrow was managed by Albert B. Grossman, who later worked in the same capacity for Bob Dylan.
In the book "Positively 4th Street" by David Hajdu, Travers recalled that Grossman's strategy was to "find a nobody that he could nurture and make famous."
The budding trio, boosted by the arrangements of Milt Okun, spent seven months rehearsing in her Greenwich Village apartment before their 1961 public debut at the Bitter End.
Their beatnik look - a tall blonde flanked by a pair of goateed guitarists - was a part of their initial appeal. As The New York Times critic Robert Shelton put it not long afterward, "Sex appeal as a keystone for a folk-song group was the idea of the group's manager ... who searched for months for `the girl' until he decided on Miss Travers."
The trio mingled their music with liberal politics, both onstage and off. Their version of "If I Had a Hammer" became an anthem for racial equality. Other hits included "Lemon Tree," "Leaving on a Jet Plane" and "Puff (The Magic Dragon.)"
They were early champions of Dylan and performed his "Blowin' in the Wind" at the March on Washington in August 1963.
And they were vehement in their opposition to the Vietnam War, managing to stay true to their liberal beliefs while creating music that resonated in the American mainstream.
The group collected five Grammy Awards for their three-part harmony on enduring songs like "Leaving on a Jet Plane," "Puff (The Magic Dragon)" and "Blowin' in the Wind."
At one point in 1963, three of their albums were in the top six Billboard best-selling LPs as they became the biggest stars of the folk revival movement.
It was heady stuff for a trio that had formed in the early 1960s in Greenwich Village, running through simple tunes like "Mary Had a Little Lamb."
Their debut album came out in 1962, and immediately scored a pair of hits with their versions of "If I Had a Hammer" and "Lemon Tree." The former won them Grammys for best folk recording and best performance by a vocal group.
"Moving" was the follow-up, including the hit tale of innocence lost, "Puff (The Magic Dragon)" - which reached No. 2 on the charts, and generated since-discounted reports that it was an ode to marijuana.
Album No. 3, "In the Wind," featured three songs by the then-22-year-old Dylan. "Don't Think Twice, It's Alright" and "Blowin' in the Wind" both reached the top 10, bringing Dylan's material to a massive audience; the latter shipped 300,000 copies during one two-week period.
"Blowin' In the Wind" became another civil rights anthem, and Peter, Paul and Mary fully embraced the cause. They marched with the Rev. Martin Luther King Jr. in Selma, Alabama, and performed with him in Washington.
In a 1966 Times interview, Travers said the three worked well together because they respected one another. "There has to be a certain amount of love just in order for you to survive together," she said. "I think a lot of groups have gone down the tubes because they were not able to relate to one another."
With the advent of the Beatles and Dylan's switch to electric guitar, the folk boom disappeared. Travers expressed disdain for folk-rock, telling the Chicago Daily News in 1966 that "it's so badly written. ... When the fad changed from folk to rock, they didn't take along any good writers."
But the trio continued their success, scoring with the tongue-in-cheek single "I Dig Rock and Roll Music," a gentle parody of the Mamas and the Papas, in 1967 and the John Denver-penned "Leaving on a Jet Plane" two years later.
They also continued as boosters for young songwriters, recording numbers written by then-little-known Gordon Lightfoot and Laura Nyro.
In 1969, the group earned their final Grammy for "Peter, Paul and Mommy," which won for best children's album. They disbanded in 1971, launching solo careers - Travers released five albums - that never achieved the heights of their collaborations.
Over the years they enjoyed several reunions, including a performance at a 1978 anti-nuclear benefit organized by Yarrow and a 35th anniversary album, "Lifelines," with fellow folkies Ramblin' Jack Elliott, Dave Van Ronk and Seeger. A boxed set of their music was released in 2004.
They remained politically active as well, performing in 1995 on the anniversary of the Kent State shootings and performing for California strawberry pickers.
Travers had undergone a successful bone marrow transplant to treat her leukemia and was able to return to performing after that.
"It was like a miracle," Travers told The Associated Press in 2006. "I'm just feeling fabulous. What's incredible is someone has given your life back. I'm out in the garden today. This time last year I was looking out a window at a hospital." She also said she told the marrow donor "how incredibly grateful I was."
But by mid-2009, Yarrow told WTOP radio in Washington that her condition had worsened again and he thought she would no longer be able to perform.
Travers lived for many years in Redding, Connecticut She is survived by her husband, Ethan Robbins, and daughters, Alicia and Erika.
Associated Press writer Polly Anderson and AP Music Writer Nekesa Mumbi Moody contributed to this report from New York.