Malcolm X's family is going after the federal government in a new lawsuit ... alleging the feds played a key role in the civil rights leader's 1965 assassination.

Three of Malcolm X's daughters filed the suit Friday on their own behalf and on behalf of his estate, claiming the CIA, FBI, DOJ and NYPD all participated in a wide-ranging conspiracy behind their father's shooting death.

In the docs, obtained by TMZ, the family claims these agencies also engaged in a decades-long coverup after Malcolm was gunned down on February 21, 1965 at the Audubon Ballroom in Manhattan.

Malcolm's family claims the CIA, FBI, DOJ and NYPD were aware of credible threats against his life leading up to his assassination ... but they did nothing to stop the murder.

The family claims former head of the FBI J. Edgar Hoover directed federal agencies to illegally surveil Malcolm X and actively conspire to reduce Malcolm's protection, leaving Malcolm vulnerable to an attack they believe Hoover knew was imminent.

As for allegations of a government cover-up... the family claims witnesses were manipulated with false facts ... and they allege the feds concealed evidence that they had known about the assassination plot.

Malcolm X's family is seeking more than $100 million in damages.

The FBI tells TMZ ... "It's the standard practice to decline to comment on ongoing litigation."