Brafman, in his letter Monday, wrote that Shkreli, 34, believes he is "being targeted" by federal prosecutors "not because of his conduct, but because of who he is." He also believes the press is focusing "unfairly on negative aspects of him" in its coverage of the case, the lawyer wrote.

"Having said that, we also note that Mr. Shkreli is under enormous pressure that is compounded by his clearly frail emotional state."

Brafman told the judge that "we have spoken to Mr. Shkreli and we will make every effort to remove this issue from the case."

"We object strongly to the gag order," the lawyer wrote. He added that if the media coverage "remains prejudicial" defense attorneys must be allowed to respond to that coverage, if necessary.

The lawyer's response in a letter to Matsumoto came after prosecutors filed a motion asking to bar Shkreli from making any more public comments about the case, either to the press, on Twitter or other social media, as long as the trial is ongoing.

Prosecutors also want defense lawyers and themselves gagged from making public comments.

Shkreli is charged with securities fraud in connection with his alleged looting millions of dollars from Retrophin, the publicly traded drug company he founded. Prosecutors claim he used the money to repay investors whom he allegedly defrauded at two hedge funds he had run, in addition to paying off personal debts.

In their motion, prosecutors cited Shkreli's surprising, impromptu meeting with reporters covering the case last Friday, among other incidents.

During that meeting, Shkreli called the prosecutors "the "junior varsity," criticized a witness against him, and lambasted headlines about the case.

Those prosecutors said Shkreli's off-the-cuff remarks, made against the desperate wishes of his lawyers, "risks tainting the jury."

Prosecutors, who believe that Shkreli has resumed posting on Twitter under a pseudonym despite being banned from the social media platform earlier this year for harassing a female reporter, also want him barred by the judge from tweeting further about the case.

If they don't get the gag order granted, prosecutors want a semi-sequestration of jurors to protect them from hearing or reading Shkreli's comments during his trial on charges of securities fraud.