He live streams regularly after returning home from court. Learning, in 2015, that he was under investigation, he voluntarily met with federal prosecutors and investigators without a lawyer, giving the government statements that are being used against him at trial. Barred from Twitter under one account, he is believed to have interacted with journalists and the public under another, @BLMBro, during the trial.

And on Friday, during a lunch break at court, he stopped by a room where several journalists were working for an on-the-record chat. He called the prosecutors on the case “junior varsity,” argued that a woman who had testified about her tangled investment in his hedge fund was not a “victim,” asked the journalists how they thought the trial was going and said his critics “blame me for capitalism,” according to CNBC. Only when Benjamin Brafman, his lawyer, entered and said, “Martin, can I see you a minute?” did Mr. Shkreli stop.

In papers filed late Monday, federal prosecutors argued that Mr. Shkreli’s public statements risked tainting the jury. They asked Judge Kiyo A. Matsumoto to restrict Mr. Shkreli from further public statements, and to consider partial sequestration of the jury.

Prosecutors cited a number of Twitter messages from the @BLMBro account that criticized evidence in the trial, arguing that there was a strong likelihood that the account is Mr. Shkreli’s despite a post saying it is run by a fan. (In fact, Mr. Shkreli could be seen posting from this account in at least one of his live streams, which has since been removed.)

The prosecutors wrote that they worried that as “he is roaming the halls of the courthouse commenting,” or as he “is riling up his social media following” to criticize the government’s case, jurors might overhear or encounter these statements.