He accused Mr Trump of bullying, misogyny and dishonesty in a scathing speech in Utah on Thursday.
Mr Trump has meanwhile mocked Mr Romney on Twitter as a “failed candidate” who should not advise on electability.
Many senior Republicans are alarmed at the prospect of Mr Trump securing the nomination for November’s election.
In the latest attack from top figures in the party, several members of the Republican national security community wrote an open letter describing Mr Trump’s “vision of American influence and power in the world” as “wildly inconsistent and unmoored in principle”.
“He swings from isolationism to military adventurism within the space of one sentence,” the letter said.
Mr Trump has sought to present himself as a “unifier”, after his victories in seven states on so-called Super Tuesday consolidated his position at the front of the race for his party’s nomination.
Mr Romney, who has been a fierce critic of Mr Trump, warned in his speech on Thursday that his policies are a threat to the Republican party and to the country as a whole.
“Here’s what I know: Donald Trump is a phony, a fraud,” Mr Romney says. “His promises are as worthless as a degree from Trump University.”
Mr Romney also warned that the nomination of Mr Trump would pave the way to the presidency for Democratic rival Hillary Clinton.
Mr Trump meanwhile accused Mr Romney of having run “one of the worst races in presidential history” and “working with the establishment” to prevent a Republican win.
Mr Romney lost the 2012 election to President Barack Obama.
Several Republican party leaders, including House Speaker Paul Ryan and South Carolina Senator Lindsey Graham, have spoken out against Donald Trump’s controversial policies and positions in recent days.
His latest controversy centres on his failure to disavow David Duke, a leader of the white supremacist Ku Klux Klan, who endorsed him. He later said he had on several occasions in the past disavowed Mr Duke.
Mr Ryan said on Tuesday that nominees “must reject any group or cause that is built on bigotry. This party does not prey on people’s prejudices”.
Senator and majority leader Mitch McConnell said: “Let me make it perfectly clear, Senate Republicans condemn David Duke and the KKK, and his racism.”
Trump rival Marco Rubio indicated in his speech on Tuesday that the Republican establishment was unlikely to back the former reality TV star.
“If this was anybody else as a front-runner, there’d be people right now saying ‘Let’s all rally around the front-runner,'” he said, adding, “that will never happen with Donald Trump”.
According to the New York Times, some party donors are already trying to raise funds for an anti-Trump effort.
Mrs Clinton also won seven states on Tuesday, consolidating her lead in the Democratic race over rival Bernie Sanders.