Washington DC - Robert Mueller, the former FBI director who led a politically explosive investigation into Donald Trump, has died aged 81, triggering a gloating response Saturday from the president.

The New York Times reported Mueller's death, citing a family statement, but did not specify a location or cause.

Trump responded quickly on Truth Social, writing: "Robert Mueller just died. Good, I'm glad he's dead. He can no longer hurt innocent people!"

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Mueller led the FBI for 12 years, starting just days before the September 11, 2001, Al-Qaeda attacks on the US, during which time he built up the bureau's counterterror mission.

After his tenure at the FBI, he was tapped as a special counsel for the Department of Justice to lead a probe between 2017 and 2019 into whether Trump's presidential campaign conspired with Russia to get him elected.

Last March, Trump sought retribution against Mueller by targeting his former law firm, WilmerHale, in an executive order, but the effort was later struck down by a judge who deemed the move unconstitutional.