(CNN) -- Joe Frazier, the hard-hitting boxing heavyweight who handed the legendary Muhammad Ali his first defeat, died Monday, just a month after being diagnosed with liver cancer, his family said in a statement.
The former heavyweight champion, who was 67, became a legend in his own right and personified the gritty working-class style of his hard-knuckled hometown, Philadelphia -- a fitting setting for the "Rocky" film series, starring Sylvester Stallone as hardscrabble boxer Rocky Balboa. Philadelphia Mayor Michael Nutter called Frazier the "quintessential Philadelphia boxer."
"You could hear him coming, snorting and grunting and puffing, like a steam engine climbing a steep grade," Bill Lyon wrote in a Philadelphia Inquirer column about Frazier, nicknamed Smokin' Joe.
"He was swarming and unrelenting, and he prided himself that he never took a backward step, and he reduced the Sweet Science to this brutal bit of elemental math: 'I'll let you hit me five times if you'll let me hit you just once.'"
Frazier's family issued a brief statement about his death.
"We The Family of ... Smokin' Joe Frazier, regret to inform you of his passing," the statement said. "He transitioned from this life as 'One of God's Men,' on the eve of November 7, 2011 at his home in Philadelphia, Pennsylvania."
Muhammad Ali said in a statement that the "world has lost a great champion."
"I will always remember Joe with respect and admiration. My sympathy goes out to his family and loved ones," Ali's statement said.
Star boxer Floyd "Money" Mayweather offered to pay for Frazier's funeral.
"My condolences go out to the family of the late great Joe Frazier," read a post on Mayweather's official Twitter feed. "#TheMoneyTeam will pay for his funeral services."
Fans and well-wishers were encouraged to post their thoughts and prayers on a Facebook page at joefrazierscorner.com.
"RIP Smokin' Joe Frazier you had heavy hands and a big heart you will be missed," read a Facebook post .
Another post said: "One of my childhood heroes has left us ...I'm really sad."
The son of a South Carolina sharecropper, Frazier boxed during the glory days of the heavyweight division, going up against greats George Foreman, Oscar Bonavena, Joe Bugner and Jimmy Ellis.
He made his name by winning a gold medal for the United States at the 1964 Summer Games in Tokyo. U.S. Olympic Committee CEO Scott Blackmun said Frazier was "one of the greatest boxers of all time" and "was an Olympic champion and an American icon."
Frazier used his devastating left hook with impunity during his professional career, retiring in 1976 with a 32-4-1 record and staging one last comeback fight in 1981.
HBO analyst and famed trainer Emanuel Steward, who knew Frazier from amateur boxing, told boxer Buster Mathis not to fight Frazier as a pro.
"And in 1968, they did, and Joe Frazier's determination and strength and pressure -- and that wicked left hook -- he broke Buster down and knocked him out," Steward said. "He was one of the most vicious machines I ever saw in my life.
But it was his three much-hyped fights against Ali that helped seal his legend.
Frazier bested Ali at 1971's "Fight of the Century" at Madison Square Garden. In the 15th round, Frazier landed perhaps the most famous left hook in history, catching Ali on the jaw and dropping the former champ for a four-count, according to Frazier's bio at the International Boxing Hall of Fame. Frazier left the ring as the undisputed champ and handed Ali his first professional loss.
"Ali was talking to him and Joe never did bow down. Ali would make a comment and Joe would talk right back. He always had that determination," Steward said.
Ali won a 12-round decision in a January 1974 rematch, setting the stage for the classic "Thrilla in Manila" just outside the Philippine capital in 1975.
Ali took the early rounds, but Frazier rebounded before losing the last five rounds. By the end of the 14th, Frazier's eyes were nearly swollen shut, and his corner stopped the bout, according to the biography.
Later, Ali said, "It was the closest I've come to death."
Philadelphia Daily News columnist Stan Hochman noted that Frazier "summoned the skill and courage to battle Ali into the 14th round in Manila."
"He was a fighter, pure and simple, with a style that seemed destined for a short career. Trudge forward, lean on the other guy, take two to land one," Hochman wrote.
"'You've gotta breathe on him,'" Frazier would say, in a rare attempt to define his style. 'No shortcuts' was his mantra. There's a lesson there for all of us," Hochman's column said Tuesday.
Boxer Mike Tyson sent Twitter messages saying the era of Frazier and Ali represented an age of "competitive fighting at the highest level."
"Each man would not give an inch until they were dead," he said, adding that "it has always been an honor to be compared" to Frazier.
Frazier, a two-time heavyweight champion for nearly three years until he lost in January 1973 to George Foreman, ran a well-known boxing gym in Philadelphia for years.
"I don't mind working with the kids," Frazier told CNN's Don Lemon in 2009. "The kids is tomorrow. And if we don't do what we're supposed to do for them now, how are you going (to) expect them to carry on?"
Asked whether he was similar to Rocky Balboa, Frazier replied, "Sure. I worked at the slaughterhouse. I'm the guy that ran in the streets of Philadelphia."
Nutter said Frazier "represented the heart and soul of boxing in our great city."
"In the ring and in the neighborhoods, he carried himself with dignity and courage. He was a true ambassador for our city. I enjoyed him as a fighter, and I really liked him as a person," the mayor said. "The entire city mourns his passing, and we keep him and his family in our prayers."
CNN's Steve Almasy contributed to this report