The cartoon, which Mr Trump deleted after tweeting, depicts the cable network logo being run over by a "Trump Train" symbolising his supporters.

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.

White House officials told NBC the train image - captioned "Fake news can't stop the Trump Train" - had been "inadvertently posted" and when "noticed it was immediately deleted".

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 Burnley, England, promptly changed his Twitter bio to read: "Officially Endorsed by the President of the United States. I wish that were a good thing."

Asked by the BBC if he thinks the "endorsement" ended when Mr Trump deleted the tweet he laughed and said: "Oh, absolutely. I don't think he really meant to endorse it.

"I don't think he intended to say, 'yup, that's me, the big ol' fascist!'"

"I'm an internet nobody!" added Mr Holden, a 53-year-old IT consultant, adding the response has been "absolutely bananas".

"It's rare you get that kind of attention from the president, isn't it?" Mr Holden added.

Mr Trump has drawn criticism from both ends of the political spectrum since Saturday's so-called Unite The Right rally in Charlottesville, Virginia, where a woman was killed.

Heather Heyer, a 32-year-old counter-protester, was killed and 19 other people were injured when a car rammed the crowd. A 20-year-old man is facing murder and other charges.

Mr Trump did not immediately condemn the white supremacists, instead blaming "many sides" for "hatred, bigotry, and violence" in the university town.

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.

Asked by journalist Jim Acosta why he had waited so long to condemn the hate groups, Mr Trump responded: "I like real news, not fake news."

Pointing the finger at the White House correspondent, he added: "You are fake news."

Mr Trump frequently targets the so-called "fake news media" in tweets to his nearly 36 million followers.

In May he shared a clip of himself pummelling professional wrestler with a CNN logo superimposed on his face.

Late on Monday, Mr Trump also retweeted a post from an account linked to one of his supporters known for fuelling conspiracy theories, such as "Pizzagate".

The post by Jack Posobiec linked to a story from an ABC affiliate and said: "Meanwhile: 39 shootings in Chicago this weekend, 9 deaths. No national media outrage. Why is that?"

The Pizzagate conspiracy theory claimed Hillary Clinton's campaign chief was running a paedophile ring out of a pizza parlour in Washington.

Mr Trump awoke for the first time as president in Trump Tower on Tuesday, tweeting that it "feels good to be home".

He arrived at the Manhattan skyscraper on Monday night amid throngs of protesters calling for his impeachment.

Three people were arrested, and police expect further demonstrations on Tuesday.

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.

"The fact that it took the president two days to clearly denounce racists and white supremacists is shameful," Mr Fallon said on his NBC show.

Meanwhile, former President Barack Obama's response on Saturday night to the Charlottesville violence is already one of Twitter's most popular posts ever.

Quoting Nelson Mandela's autobiography, Mr Obama tweeted: "No one is born hating another person because of the color of his skin or his background or his religion..."

The tweet had more than 2.5m likes by Tuesday, making it the second most-liked tweet of all time.

Pop star Ariana Grande's post following a deadly bombing at her concert in England remains the most popular tweet of all time, with 2.7m likes.