Later, CNN said it had also rejected another Trump ad, “Coup,” which presents the impeachment inquiry as an effort “to undo the election, regardless of facts,” and accuses House Democrats of “fabricating evidence.”

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“The ad contains assertions of fact about the whistle-blower complaint that have been refuted by the Intelligence inspector general,” CNN said. “In addition, it is inaccurate to use the word ‘coup’ to describe a constitutionally prescribed legal process.”

[Read more about “coup” claims used by Mr. Trump’s supporters.]

The moves by CNN are likely to inflame longstanding tensions between the news channel and the president, who denounced the network at multiple public appearances this week. At a White House news conference on Wednesday, Mr. Trump called CNN staff members “corrupt people.”

CNN said it had agreed to carry a third commercial submitted by the Trump campaign, which focuses on the president’s accomplishments in office.

Mr. Trump has said his request for help digging into the Bidens was legitimate and part of a “perfect” phone call with President Volodymyr Zelensky of Ukraine. On Thursday, Mr. Trump publicly asked China to investigate the former vice president.

The impeachment inquiry has spurred a surge in campaign spending since it was announced on Sept. 24. Need to Impeach, a group founded and funded mainly by the billionaire Democratic presidential candidate Tom Steyer, said this week that it planned to spend $3.1 million on television and digital ads urging Republican senators to remove Mr. Trump.

The Trump campaign has spent more than $1.6 million to advertise on Mr. Trump’s Facebook page in the past seven days, including as much as $21,000 on the “Biden Corruption” ad, according to the platform’s ad library. Facebook does not fact-check speech from politicians, generally allowing it on the platform “even when it would otherwise break our normal content rules,” Nick Clegg, a Facebook executive and former British deputy prime minister, said in Washington last week.