"I hope to see the Republican Party assume once again the mantle of being the party of Lincoln. It upsets me that our energies as a society are being sapped by the President's culture of divisiveness in Washington," he said Friday in New Hampshire, adding later, "Because of the many concerns I've talked about today, I've established an exploratory committee ... as a Republican in the 2020 election."
Speaking at the "Politics & Eggs" breakfast in Bedford, New Hampshire, Weld called Donald Trump a "schoolyard bully," "unstable" and "a president whose priorities are skewed to the promotion of himself rather than toward the good of the country."
Though a number of Democratic candidates have joined the 2020 race in hopes of ultimately facing off against Trump in the general election, Weld is the first potential primary challenger to the President.
"The truth is that we've wasted an enormous amount of time by humoring this President, indulging him in his narcissism and his compulsive irrational behaviors," Weld said Friday, saying Republicans in Washington show "the symptoms of Stockholm syndrome."
He added, "The situation is not yet hopeless, but we do need a mid-course correction."
Weld has had a unique political path. He served as a two-term Massachusetts governor during the early 1990s and later lost the 1996 US Senate race in Massachusetts against John Kerry.
Weld later moved to New York and unsuccessfully sought the Republican nomination for governor in 2005.
He was Mitt Romney's co-chair in New York when Romney ran for president in 2008. After Romney dropped out, Weld ended up endorsing then-Democratic nominee Barack Obama for president over the GOP nominee, Sen. John McCain.
Weld was the 2016 vice presidential nominee on the Libertarian Party ticket with former New Mexico Gov. Gary Johnson.
CNN's Dominique Robertson contributed to this report.