There are worse mistakes an organisation armed with nuclear missiles can make, but Thursday's online Pentagon gaffe was plenty embarrassing.

The Department of Defense mistakenly retweeted an anti-Trump message that demanded the president's resignation.

The Pentagon quickly disavowed the retweet and explained that it was a mistake, removing it, according to the Daily Mail.

But the liberal protester who sent the tweet into cyberspace is having a field day with the disruption.

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The tweet, from unidentified Twitter user @ProudResister, equated Trump with other politicians who have drawn accusations of sexual misconduct that date back to before their political careers.

"The solution is simple," it read. "Roy Moore: Step down from the race. Al Franken: Resign from congress. Donald Trump: Resign from the presidency. GOP: Stop making sexual assault a partisan issue. It's a crime as is your hypocrisy."

Chief Pentagon Spokesperson Dana White explained how an anti-Trump message made its way to the Defense Department's 5.2 million followers.

"An authorized operator of the @DeptofDefense's official Twitter site erroneously retweeted content that would not be endorsed by the Department of Defense,' she wrote in a new tweet.

"The operator caught this error and immediately deleted it."

The @ProudResister account is run by a Los Angeles, California man who identifies himself on Facebook as Ryan Knight.

Among his Facebook posts are some that identify Barack Obama as a "patriot" and Donald Trump as a "traitor."

Another claims that while "ObamaCare" and "NFL players kneeling" offend Republicans, "pedophiles" and "white hoods" do not.

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Knight's Twitter profile points to a commercial apparel business that sells a $23 t-shirt reading: "All I want for Xmas is a new president."

Another offering, a $26 sweatshirt, drops nine separate f-bombs.

They include claims that President Trump wants to "f**k America" and that his spokeswoman, White House press secretary Sarah Huckabee Sanders, aims to "f**k the truth."