Judge Eric Davis also said an investigation was likely into Fox’s handling of documents and whether it had withheld details about Rupert Murdoch’s corporate role.

The judge overseeing Dominion Voting Systems’ lawsuit against Fox News said on Wednesday that he was imposing a sanction on the network and would very likely start an investigation into whether Fox’s legal team had deliberately withheld evidence, scolding the lawyers for not being “straightforward” with him.

The rebuke came after lawyers for Dominion, which is suing for defamation, revealed a number of instances in which Fox’s lawyers had not turned over evidence in a timely manner. That evidence included recordings of the Fox News host Maria Bartiromo talking with former President Donald J. Trump’s lawyers, Sidney Powell and Rudy Giuliani, which Dominion said had been turned over only a week ago.

In imposing the sanction on Fox, Judge Eric M. Davis of the Delaware Superior Court ruled that if Dominion had to do additional depositions, or redo any, then Fox would have to “do everything they can to make the person available, and it will be at a cost to Fox.”

He also said he would very likely appoint a special master — an outside lawyer — to investigate Fox’s handling of discovery of documents and the question of whether Fox had inappropriately withheld details about the scope of Rupert Murdoch’s role. Since Dominion filed its suit in early 2021, Fox had argued that Mr. Murdoch and Fox Corporation, the parent company, should not be part of the case because Mr. Murdoch, the chair, and other senior executives had nothing to do with running Fox News. But in the past few days, Fox disclosed to Dominion that Mr. Murdoch was a corporate officer at Fox News.

Dominion, a voting technology company, accused Fox and some of the network’s executives and hosts of smearing its reputation by linking it to a nonexistent conspiracy to rig voting machines in the 2020 presidential election. Fox had said that it was just reporting on newsworthy allegations from Mr. Trump, who was then the president, as well as his lawyers and supporters, who told Fox’s hosts and producers that they would prove their allegations in court.

Jury selection starts on Thursday, and the trial is scheduled to begin on Monday. It wasn’t immediately clear whether Dominion would avail itself of the judge’s ruling allowing its lawyers to conduct additional depositions. But it was clear from Judge Davis’s stern reprimand of Fox’s lawyers on Wednesday — and similarly piqued remarks from him during another hearing on Tuesday — that he was losing patience.

The judge told Fox’s lawyers to retain all internal communications, starting from March 20 of this year, that related to Mr. Murdoch’s role at Fox News. That was the date the lawyers submitted a letter to Judge Davis asking that Mr. Murdoch and other Fox Corporation executives not be forced to testify at the trial in person, saying they had “limited knowledge of pertinent facts.” The letter did not mention that Mr. Murdoch was also a Fox News executive.

Judge Davis said he would weigh whether any additional sanctions should be placed on Fox.

He also said he was very concerned that there had been “misrepresentations to the court.”

“This is very serious,” Judge Davis said.

Davida Brook, a lawyer for Dominion, told the court that they were still receiving relevant documents from Fox, with the trial just days away.

“We keep on learning about more relevant information from individuals other than Fox,” she said. “And to be honest we don’t really know what to do about that, but that is the situation we find ourselves in.”

She pointed to one email that had recently been handed over, between Ms. Bartiromo and Ms. Powell on Nov. 7, 2020. In the email, Ms. Powell was forwarding evidence to Ms. Bartiromo that Dominion said was proof Fox had acted recklessly: an email from a woman Ms. Powell relied on as a source who exhibited signs of delusion, claiming, for instance, that she was aware of voter fraud because she had special powers, including the ability to time travel.

“I just spoke to Eric and told him you gave very imp info,” Ms. Bartiromo wrote back to Ms. Powell, most likely referring to Eric Trump, Mr. Trump’s son.

Ms. Brook also played two recordings for the court of pre-interviews, which are preliminary conversations before an on-air interview, conducted by Ms. Bartiromo that Ms. Brook said were received only after they were revealed in legal complaints filed by Abby Grossberg, a former Fox News producer who is suing the network.

In one of the recordings, on Nov. 8, 2020, Ms. Bartiromo asks Mr. Giuliani about Dominion’s software. In it, he admits that he doesn’t have hard evidence to back up the claim that the software could be manipulated, saying it was “being analyzed right now.” When Ms. Bartiromo asks about a conspiracy theory circulating at the time that claimed Dominion was connected to Representative Nancy Pelosi of California, Mr. Giuliani says: “Yeah, I’ve read that. I can’t prove that yet.”

A Fox News spokeswoman said in a statement on Wednesday: “As counsel explained to the court, Fox produced the supplemental information from Ms. Grossberg when we first learned it.”

Justin Nelson, another lawyer for Dominion, told Judge Davis that had Fox Corporation, the parent company, been quicker to share the information about Mr. Murdoch’s role as an officer of Fox News, the universe of documents Dominion could have obtained during discovery from him and other Fox Corporation executives would have been much larger. He also said that Fox might have failed to produce relevant documents.

“We have been litigating based upon this false premise that Rupert Murdoch wasn’t an officer of Fox News,” he said.

The question of whether Mr. Murdoch made decisions as a corporate officer of Fox News cuts to the heart of Dominion’s case. It has tried to prove — and Fox has repeatedly denied — that Rupert and Lachlan Murdoch, the chief executive of Fox Corporation, were closely involved in overseeing Fox News coverage of the 2020 election. Their decisions, Dominion has argued, directly affected what Fox broadcast about the voting technology company and, more broadly, fed a climate inside the network where hosts and producers amplified misinformation as part of a plan to win back viewers who had stopped watching after Mr. Trump’s loss.

Proving so would mean that the larger Fox Corporation — not just Fox News — could also be found liable for defaming Dominion.

Mr. Nelson argued that the case should be split in two so that Dominion lawyers could separately pursue action against Fox Corporation now that Dominion could obtain more information from executives. Judge Davis declined, but he expressed concern that Fox’s legal team had not been forthcoming with the information, despite being asked multiple times whether Mr. Murdoch was a corporate officer for Fox News.

“I need people to tell me the truth,” he said. “And by the way, omission is a lie.”

Dan K. Webb, a lawyer for Fox, pushed back on the assertion from Dominion, saying that both he and even Mr. Murdoch didn’t realize he also held the executive chair role at Fox News.

“On a day-to-day basis, Mr. Rupert Murdoch had nothing to do with making decisions with what goes on the air on Fox News,” Mr. Webb said.

In an emailed statement, a Fox News spokeswoman said: “Rupert Murdoch has been listed as executive chairman of Fox News in our S.E.C. filings since 2019 and this filing was referenced by Dominion’s own attorney during his deposition.”

Judge Davis admonished Fox’s lawyers, saying he had previously asked for clarity on who had corporate responsibilities at Fox News but had not heard back.

“What do I do with attorneys that aren’t straightforward with me?” he asked.