The Utah senator and former presidential nominee said he was taking advice on self-isolation after spending time on Friday with Rand Paul, who announced on Sunday that he had tested positive for Covid-19.
Told during a White House briefing that Mr Romney was one of several politicians self-isolating, the president said: “Romney’s in isolation? Gee, that’s too bad.”
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A reporter asked him: “Do I detect sarcasm there?”
Mr Trump shook his head and said: “No, no, none whatsoever.”
More than 400 people have died from Covid-19 in the United States, with more than 32,000 cases identified.
MSNBC host Chris Hayes responded to Mr Trump’s comment by tweeting: “Super funny joke! One of our incredible colleagues died from this on Friday.” Larry Edgeworth, an NBC employee who worked in an equipment room at the broadcaster’s headquarters in New York, died last week.
Mr Romney has become a hate figure for the president and his supporters since becoming the lone Republican to vote for Mr Trump’s conviction for abuse of power, one of the two charges he faced after being impeached by the House of Representatives.
The president was accused of secretly trying to pressure a vulnerable ally into inteferring in the 2020 election by smearing Democratic frontrunner Joe Biden.
Following his acquittal by Republican allies in the Senate, Mr Trump tweeted: “Had failed presidential candidate @MittRomney devoted the same energy and anger to defeating a faltering Barack Obama as he sanctimoniously does to me, he could have won the election. Read the Transcripts!”
At a prayer breakfast he lambasted the senator again, referring to his justification of his impeachment vote because of his Mormon faith. Mr Trump said: “I don’t like people who use their faith as justification for doing what they know is wrong.”
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At the CPAC conference of conservative activists, Mr Romney’s name was repeatedly booed.
On Sunday morning Mr Paul, a GOP senator for Kentucky, tweeted a statement reading: “A statement on his Twitter account read: “Senator Rand Paul has tested positive for COVID-19. He is feeling fine and is in quarantine. He is asymptomatic and was tested out of an abundance of caution due to his extensive travel and events. He was not aware of any direct contact with any infected person.
“He expects to be back in the Senate after his quarantine period ends and will continue to work for the people of Kentucky at this difficult time. Ten days ago, our DC office began operating remotely, hence virtually no staff has had contact with Senator Rand Paul.”