Romney, the 2012 Republican presidential nominee, on Thursday in Salt Lake City, Utah, calling him "a phony, a fraud" and saying it is his "very brand of anger that has led other nations into the abyss."
The speech by Romney, the former Massachusetts governor, was the latest illustration of how badly many mainstream Republican leaders want to stop Trump, the clear front-runner, from becoming his party's nominee in November's election to succeed President Barack Obama.
Twitter users posted about Romney roughly 38 times per second following the speech, according to Zoomph, the social media analytics firm.
Romney's sentiment score, a measure of how positively users discuss a topic, was slightly higher than Trump's following the speech, according to Zoomph.
'Mitt Romney' quickly became one of the top-trending topics on Twitter in the US.
As of noon there were about 153,000 tweets about Romney on Twitter, according to the social media site’s own metrics.
During a campaign rally in Maine, Trump said Romney had begged Trump to endorse his 2012 presidential campaign. His comments included what many on social media perceived to be a crude sexual joke.
"I could have said 'Mitt, drop to your knees,' he would have dropped to his knees," Trump said.
"Is this a new @realDonaldTrump campaign slogan? 'Drop to Your Knees, America ... and they did,'" tweeted Carl Spry (@CarlSpry). "His secret to getting so many endorsements?".
In his speech criticizing both Trump's policy proposals and his style, Romney did not endorse any of the candidates remaining in the Republican race.
But one of them, Ohio Governor John Kasich (@JohnKasich), tweeted his support, saying "Well said, @MittRomney."
A photo of the presidential Oval Office accompanied the tweet, with the caption "The One Who Works Here Should Make Us Proud."
Other presidential candidates remained quiet on Twitter, but Republican South Carolina Governor Nikki Haley offered her support for Romney.
"A brilliant speech by @MittRomney. No one can ever question his love for our party and our country. #TrueLeadership #MittRomney," she (@nikkihaley) tweeted.
Haley has endorsed Marco Rubio, a US senator from Florida, for the Republican nomination.
Some social media users, however, noted that Romney had accepted an endorsement from Trump during his failed 2012 presidential campaign and argued this undermined Romney's critique.
"Erm ... does Mr Romney have amnesia?" tweeted television personality Piers Morgan (@piersmorgan) Thursday.
Kevin Madden (@KevinMaddenDC), an adviser to Romney in 2012, tweeted "Mistake, imo [in my opinion], to not directly address/express regret over 2012 endorsement."
