Some of Mr. Trump’s former aides testified that the Fox call shocked them but also undermined their confidence in his chances of victory. Jason Miller, a senior aide on the Trump campaign, said in video testimony played by the committee that he and others were “disappointed with Fox” for making the call but at the same time “concerned that maybe our data or our numbers weren’t accurate.”

Mr. Miller had shared none of that concern on election night, when he tweeted that Fox was a “complete outlier” whose call should be ignored by other media. At Mr. Trump’s insistence, he and other aides immediately reached out to Fox executives, producers and on-air talent to demand an explanation. Jared Kushner, Mr. Trump’s son-in-law, went straight to the top, calling Mr. Murdoch. The scene played out in part on the air as Fox talent commented about the complaints raining down on them from the Trump campaign.

“Arnon, we’re getting a lot of incoming here, and we need you to answer some questions,” the network’s chief political anchor, Bret Baier, said at one point, referring to Arnon Mishkin, the person on the decision desk who was responsible for analyzing the data and recommending when Fox issue its calls.

On Monday, Mr. Stirewalt did not describe either Mr. Murdoch or Lachlan Murdoch, the Fox Corporation executive chairman, as being part of the decision desk’s process. And network executives have said the Murdochs were not involved.

Though Fox News coverage is typically favorable to conservative, pro-Trump points of view, that deference has never been adopted by the decision desk, which is a separate part of the news-gathering operation overseen by Mr. Mishkin, a polling expert who is also a registered Democrat. In the days after the election, Mr. Mishkin was unwavering in his defense of the call as Fox anchors pressed him. Once, as the host Martha MacCallum peppered Mr. Mishkin with a series of “what if” scenarios that could bolster Mr. Trump’s chances of eking out a victory, Mr. Mishkin responded sarcastically, “What if frogs had wings?” (Mr. Mishkin remains a paid consultant for the network, not an employee, and will run the decision desk for the midterm elections in November.)

The decision desk was created under the former Fox News chairman and founder Roger Ailes, who relished making controversy and drawing ratings more than he cared about toeing the line for the Republican Party. Its quick calls angered Republicans on more than one occasion, including in 2012, when it was the first to project that President Barack Obama would win Ohio and a second term, and in 2018 when it declared that Republicans would lose the House of Representatives even as votes were still being cast on the West Coast.