The civil rights activist and prominent figure in the Nation of Islam was killed at the Audubon Ballroom in Manhattan in February 1965.
The family members and Crump said the allegations were in a deathbed letter by a former police officer, Raymond Wood.
In the January 25, 2011 letter, Wood, who was on duty the day of Malcolm X's death, said he "participated in actions that in hindsight were deplorable and detrimental to the advancement of my own black people."
"Under the direction of my handlers, I was told to encourage leaders and members of the civil rights groups to commit felonious acts," Wood said in the letter.
Wood stated he was coerced by his NYPD supervisors to entice members of Malcolm X's security detail into committing crimes that resulted in their arrest days before the deadly shooting.
"It was my assignment to draw the two men into a felonious federal crime so that they could be arrested by the FBI and kept away from managing Malcolm X's door security on February 21, 1965," Wood wrote. "At that time, I was not aware that Malcolm X was the target."
Those arrests were a part of conspiracy between the NYPD and FBI to have Malcolm X killed, according to the letter.
Malcolm X was a human rights activist and prominent Black nationalist leader who served as a spokesman for the Nation of Islam, an African-American Muslim group that embraced Black separatism, during the 1950s and 1960s. A skilled orator, Malcolm X encouraged Black people to fight against racism by any means necessary.
The civil rights leader broke with the Nation of Islam shortly before his assassination at the ballroom, where he was preparing to address the Organization of Afro-American Unity. Three members of the Nation of Islam were convicted in the shooting.
The office of Manhattan District Attorney Cy Vance started reviewing the convictions last year.
After Saturday's news conference, Vance's office released a statement saying its "review of this matter is active and ongoing." The NYPD also provided a statement saying it has "provided all available records relevant to that case to the District Attorney" and "remains committed to assist with that review in any way."
Malcolm X's daughter, Ilyasah Shabazz, said she has always had uncertainty in regards to her father's death.
"Any evidence that provides greater insight into the truth behind that terrible tragedy should be thoroughly investigated," she said at the news conference.
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