Attallah Shabazz later issued a statement thanking Farrakhan for acknowledging his role and said: "I wish him peace."
Shabazz, then 6, saw her father gunned down in the Audobon Ballroom in New York's Harlem area on February 21, 1965. Three men with ties to the Nation of Islam were convicted in the slaying.
A year earlier, Malcolm X's criticism of Nation of Islam spiritual leader Elijah Muhammad had caused a bitter split with church leaders, including Farrakhan. Farrakhan called Malcolm X a traitor and wrote, two months before the killing, that "such a man is worthy of death."
Farrakhan has denied ordering the assassination but previously admitted to having "helped create the atmosphere" that led to it.
His four-hour meeting with Shabazz and "60 Minutes" correspondent Mike Wallace, organized at her request, took place at Farrakhan's home in Arizona.
Farrakhan told them that he "truly loved" Malcolm X and carried his picture after his death. Shabazz's body visibly stiffened, arms crossed over her chest, when Wallace quoted from Farrakhan's writings about Malcolm X before he died.
During the interview, Farrakhan said that the U.S. government spied on black leaders and were concerned about a "black messiah" who could unite the community. "This is bigger than the Nation of Islam," he said.
Shabazz, struggling to keep control of her emotions, said that while she believed the FBI had something to do with her father's death, it was young black men who shot him.
"You can't keep pointing fingers," she said. "My father was not killed from a grassy knoll."
Farrakhan said: "Yes, it is true that black men pulled the trigger. We cannot deny any responsibility in this. Where we are responsible, where our hands are a part of this, we beg God's mercy and forgiveness."
"I genuinely hope that perhaps a healing can come to Miss Shabazz and her family," he continued. "As I may have been complicit in words that I spoke leading up to February 21, I acknowledge that and regret that any word that I have said caused the loss of life of a human being."
Shabazz's reaction to these words isn't shown. Wallace said she needed time to absorb them. She issued a statement this week.
"He's never admitted this before publicly," she said. "Until now, he's never caressed my father's children. I thank him for acknowledging his culpability, and I wish him peace."
Shabazz's mother, Betty Shabazz, who died in 1997, had publicly accused Farrakhan of a role in the murder. She reconciled with him after her daughter Qubilah was charged in 1994 with plotting to hire a hitman to kill him. The charges were later dropped.
Wallace said he believed that Farrakhan, who has battled prostate cancer and other health problems, is making amends partly because he has faced his own mortality.
Earlier this year, Farrakhan publicly embraced W. Deen Mohammed, son of Elijah Muhammad, in an attempt to heal wounds that have split African-American Muslims into competing factions.
"I think that he has thought seriously about the people he has disaffected," Wallace said in an interview.
Shabazz said it was still difficult for her to meet with Farrakhan on camera. "I did not know if I wanted to sit across from him," she said. "I did not know if my heart could handle it."
