Marc Racicot made the statement during an interview Tuesday on Yellowstone Public Radio with Home Ground host Brian Kahn.
Racicot, 72, served two terms as governor after being elected in 1992 and again 1996. He was chairman of the RNC in 2002 and 2003 before becoming chairman of George W. Bush's 2004 re-election campaign.
Racicot said Trump lacks the patience and humility needed to lead the country.
He added: “But at the end, the content of a man's character or a woman's character to serve in that capacity is more important than any other issue that I have to consider as a matter of conscience.”
Racicot said he did not vote for Trump in 2016 and has “even more grave doubts than I did in 2016.”
He did not say who he voted for in 2016.