US presidential candidate Donald Trump has neither "the temperament nor the judgement to be president", fellow Republican Mitt Romney says.
He accused Mr Trump of bullying, misogyny and dishonesty in a speech in Utah on Thursday.
"Prospects for a safe and prosperous future are greatly diminished" if Mr Trump becomes the nominee, he added.
Mr Trump has meanwhile mocked Mr Romney as a "failed candidate" and a "choke artist".
"I backed Mitt Romney," said Mr Trump, addressing a crowd in Maine. "You can see how loyal he is, he was begging for my endorsement."
He said Mr Romney ran "the worst campaign ever" and should have beaten Barack Obama in 2012.
Many senior Republicans are alarmed at the prospect of Mr Trump securing the nomination for November's election.
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.
Analysis - Barbara Plett Usher, BBC News, Washington
In any other election season, such a public and scathing take-down of the Republican front-runner by a party stalwart would have been absolutely extraordinary.
But the rise of Donald Trump has upended political norms, and the Republican establishment is now panicking about the prospect of a presidential candidate who wants to tear up trade deals and ban Muslims from the US.
Mitt Romney declared Trump unfit to lead, warning that the billionaire's policies would lead to economic recession and make America and the world less safe, and that his nomination would hand the White House to the Democrats.
Other senior politicians have also begun to speak out and some business leaders are pumping millions of dollars into adverts attacking Mr Trump.
The aim is to prevent him from getting enough votes to secure the nomination outright in crucial contests this month, pushing the ultimate decision to the Republican National Convention in July. The strategy could backfire though, among supporters who back Mr Trump precisely because of his outsider status.
The 2008 presidential nominee, John McCain, has also joined the verbal attack on the Republican front-runner, describing Mr Trump's statements on national security as "uninformed and dangerous".
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.
He criticised the billionaire's policies on tax and promises to launch a trade war, seeking to discredit Mr Trump's business credentials by citing his history of bankruptcies.
"Here's what I know: Donald Trump is a phoney, a fraud," Mr Romney says. "His promises are as worthless as a degree from Trump University."
He attacked Mr Trump's controversial immigration policies, saying he was creating "scapegoats of Muslims and Mexican immigrants" - in reference to the former reality TV star's proposal to build a wall between America and Mexico and halt all immigration of non-citizen Muslims into the US.
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.
Ahead of the speech, he called Mr Romney "a failed candidate" who had "begged" him for an endorsement in 2012 campaign, which the former Massachusetts governor lost to Barack Obama.
- Donald Trump (Republican): Alabama, Georgia, Massachusetts, Tennessee, Virginia, Arkansas, Vermont
- Ted Cruz (Republican): Texas, Oklahoma, Alaska
- Marco Rubio (Republican): Minnesota
- Hillary Clinton (Democrat): Alabama, Georgia, Tennessee, Virginia, Arkansas, Texas, Massachusetts, and the South Pacific territory of American Samoa
- Bernie Sanders (Democrat): Vermont, Oklahoma, Minnesota, Colorado
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.