The 73-year-old businessman told an audience on Friday in New Hampshire - site of the first primary next year - that the country is in “grave peril” and that he “cannot sit quietly on the sidelines any longer”.
“We have a president whose priorities are skewed toward promotion of himself rather than toward the good of the country,” he said, according to the Boston Herald.
Mr Weld, who was the Libertarian Party’s nominee for vice-president in the 2016 election, becomes the first Republican to announce a possible challenge to Mr Trump for the Republican nomination.
An official run could spell trouble for Mr Trump, even if he was to defeat Mr Weld in a primary contest. The last three presidents who have faced one – Gerald Ford in ’76, Jimmy Carter in ’80 and George W Bush in ’92 – went on to lose the general election.
Mr Weld’s announcement comes amid an attempt by Mr Trump’s re-election campaign to change party rules to hurt any internal challenges in the upcoming election.
The state-by-state effort by aides would make it more difficult for challengers to send anti-Trump delegates to the national Republican nominating convention in August 2020.
Mr Weld, a fiscally conservative but socially liberal former federal prosecutor, re-registered as a Republican last month following his stint in the Libertarian Party.
In his speech, he called out members of his own party who “exhibit all the symptoms of Stockholm Syndrome, identifying with their captor”.
“The truth is that we have wasted an enormous amount of time by humoring this president, indulging him in his narcissism and his compulsive, irrational behavior,” he said.
In a statement, New Hampshire Republican Party chairman Stephen Stepanek condemned Mr Weld’s announcement.
“The Republican Party is a big tent, but someone who endorsed Barack Obama in 2008 and 2012 and supported Hillary Clinton in 2016 as the Libertarian Party’s vice-presidential nominee really needs to think about how welcome he is in the Republican Party,” he said.
“Bill Weld declared he would be ‘Libertarian for life’ ... and within three years he’s switched back to being a Republican to run against our president.
“In 2016, he also bragged about giving Hillary Clinton a win in New Hampshire – I don’t expect his campaign to get very far among Republican primary voters.”
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