Mr Cheney’s remarks were welcomed by the Harris camp.
“The vice-president is proud to have the support of Vice-President Cheney, and deeply respects his courage to put country over party,” said campaign chair Jen O’Malley Dillon.
Mr Cheney joins a growing list of Republicans who have expressed concern about the candidacy of Donald Trump.
His daughter, Liz Cheney, has already given her backing to Vice-President Harris.
She served on the House select committee investigating the 6 January Capitol riots, and was one of 10 Republicans to vote to impeach former President Trump after the incident.
Ms Cheney lost her seat in Congress in 2022 to a Trump-backed candidate.
Taking to social media following Mr Cheney’s statement, Trump called the former vice-president an “irrelevant RINO” – an acronym which stands for “Republican in name only”.
He also described Mr Cheney as the “King of Endless, Nonsensical Wars” – alluding to his role in the Iraq War.
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