Recently, Fox News personalities have questioned the validity of efforts by House Democrats to impeach the president. They have also helped draw attention to the debunked theory that Ukraine interfered in the 2016 election to aid Democrats, a theory favored by Mr. Trump but which contradicts the findings of American intelligence communities and the Mueller report that Russia intervened in the election to help Republicans. And anchors such as Sean Hannity and Laura Ingraham have remained vocally supportive of the president.

Nonetheless, Mr. Trump believes that the network has become more critical of him, and he has grown increasingly critical of Fox News, denouncing some anchors and reporters he does not consider to be friendly to him, such as Shepard Smith and even Ed Henry, with whom he held a recent interview. And while Mr. Trump talks frequently with Tucker Carlson, another Fox News host, Mr. Carlson has been critical of Mr. Trump’s July call with the president of Ukraine, which prompted the impeachment inquiry. Mr. Carlson said in a column for The Daily Caller website that there was “no way” to spin what took place on that call as a positive for Mr. Trump.

On Thursday morning, Mr. Trump lashed out at Fox News over a poll it commissioned on attitudes toward the impeachment inquiry.

The poll showed that 51 percent of people surveyed believe that Mr. Trump should be impeached and removed from office. Another 4 percent said he should be impeached but not removed, and 40 percent said they are against impeaching Mr. Trump.

“From the day I announced I was running for President, I have NEVER had a good @FoxNews Poll. Whoever their Pollster is, they suck,” Mr. Trump posted on Twitter. “But @FoxNews is also much different than it used to be in the good old days.”