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Roger Stone has apologised to a US judge after posting on Instagram an image of her next to what appeared to be the cross-hairs of a gun sight.

The ex-Trump campaign adviser was arrested in January and charged with seven counts as part of Robert Mueller's investigation into Russian interference in the 2016 US presidential election.

In a comment alongside the image of Judge Jackson, who is overseeing his trial, Mr Stone called the special counsel a "deep state hit-man".

Mr Stone's post, now taken down, also called the legal proceedings a "show trial" and Judge Jackson "a [former US President Barack] Obama appointed judge who dismissed the Benghazi charges against Hillary Clinton".

In 2017, Judge Jackson dismissed legal action against Mrs Clinton taken by the parents of two of the four Americans killed in a 2012 attack on the US consulate in Libya.

Judge Jackson also dismissed a related claim Mrs Clinton, who was US secretary of State at the time, had defamed the parents by lying about them in the press.

In a letter filed with the court, Mr Stone wrote: "Please inform the court that the photograph and comment today was improper and should not have been posted.

"I had no intention of disrespecting the court and humbly apologise to the court for the transgression."

He also posted on Instagram: "A photo of Judge Jackson posted on my Instagram has been misinterpreted.

"This was a random photo taken from the internet.

"Any inference that this was meant to somehow threaten the judge or disrespect court is categorically false."

Stone has been ordered to appear at a hearing on the 21st to explain the social media post.

"Defendant is ordered to show cause at a hearing to be held on Thursday 21, 2019" stated an electronic filing signed by Judge Berman.