For much of this week, after a federal judge temporarily froze the gag order she imposed on him, former President Donald J. Trump has acted like a mischievous latchkey kid, making the most of his unsupervised stint.

At least three times in the past three days, he has attacked Jack Smith, the special counsel leading his federal prosecutions, as “deranged.” Twice, he has weighed in about testimony attributed to his former chief of staff Mark Meadows, who could be a witness in the federal case accusing him of conspiring to overturn the 2020 election.

Each of Mr. Trump’s comments appeared to violate the gag order put in place less than two weeks ago to limit his ability to intimidate witnesses in the case, assail prosecutors or otherwise disrupt the proceeding. And after the former president was fined $10,000 on Wednesday for flouting a similar directive imposed on him by the judge presiding over a civil trial he is facing in New York, federal prosecutors asked that he face consequences for his remarks about the election interference case as well.

On Friday, the judge who imposed the federal order, Tanya S. Chutkan, put it on hold for a week to allow the special counsel’s office and lawyers for Mr. Trump to file more papers about whether she should set it aside for an even longer period as an appeals court considers its merits.