The president also apparently accidentally retweeted a post by someone calling him “a fascist”.
Mr Trump is in New York where he faces a second day of protests.
In another presumably unintentional retweet, the US president shared – and then also deleted – a post by someone who said of him: “He’s a fascist, so not unusual.”
The Twitter user, @MikeHolden, had been commenting on a Fox report saying that Mr Trump could be planning to pardon Arizona Sheriff Joe Arpaio, who was found guilty in July of racially profiling Hispanic people.
Mr Holden, of Manchester, England, promptly changed his Twitter bio to read: “Officially Endorsed by the President of the United States. I wish that were a good thing.”
Heather Heyer, a 32-year-old counter-protester and 19 other people were injured when a car rammed the crowd. A 20-year-old man is facing murder and other charges.
On Monday he sought to clarify his views, denouncing the Ku Klux Klan and neo-Nazis by name.
But in the process he took a moment to demean a CNN reporter.
Pointing the finger at the White House correspondent, he added: “You are fake news.”
In May he shared a clip of himself pummelling professional wrestler with a CNN logo superimposed on his face.
Late-night show hosts turned their fire on Mr Trump on Monday night.
The Tonight Show’s Jimmy Fallon, who usually avoids political polemic, rebuked the president.