Mr Trump later invited Mr Romney to visit him during the presidential transition period before the inauguration, fueling speculation that the former MA governor was being considered to be Mr Trump's Secretary of State.
"He has neither the temperament nor the judgment to be president", Romney said.
Romney's designs on the Utah seat were known well before he announced last week.
Some of that tension appeared to wane after reports that Trump was considering Romney to be his secretary of state, but the president has reportedly remained wary of Romney's allegiances and lobbied heavily for Hatch to run for re-election rather than retire.
President Trump endorsed one-time rival, and former GOP presidential candidate, Mitt Romney in his bid for a US Senate seat in Utah. "And on Utah's Capitol Hill, people treat one another with respect", said Romney.
Republican Mitt Romney is shaking hands and taking selfies with excited college students as he starts collecting voter signatures for his Utah Senate campaign.
The former presidential nominee made his campaign official Friday in an online video after a delaying his launch following a deadly shooting at a Florida high school.
Romney announced Friday he would run to replace retiring Senator Orrin Hatch.
Romney demurred when asked if he'd seek or accept Trump's endorsement and said he's focusing his campaign on Utah, where he moved with his wife, Ann, after losing the 2012 presidential election to incumbent Democrat Barack Obama.
They say Romney will suggest Washington has much to learn from the state the former MA governor now calls home. Romney, the son of former Michigan Governor George Romney, helped found the buyout firm Bain Capital and gained prominence after stepping in to lead the organizing committee for the 2002 Salt Lake City Winter Olympics after a bribery scandal. In 2016 Trump said the former MA governor had "choked like a dog" during his failed 2012 bid against President Barack Obama.