Tensions within CNN over coverage of former President Donald J. Trump burst into the open on Thursday during an internal call with the network’s journalists, as an executive candidly questioned the approach of the channel’s new chief executive, Mark Thompson.

CNN aired roughly 10 minutes of Mr. Trump’s victory speech after he won the Iowa caucuses on Monday before cutting away. The decision to cut him off prompted derision from the former president and his allies, although critics on the left questioned why CNN had taken Mr. Trump live in the first place, given his tendency to spread falsehoods and conspiracies. MSNBC chose not to take any of his remarks live.

Mr. Thompson opened his morning conference call on Thursday by acknowledging a debate within his newsroom, saying he believed the network had a journalistic obligation to broadcast the remarks of the leading Republican candidate for president.

After a period of silence, a senior vice president of programming, Jim Murphy, jumped in, telling Mr. Thompson that the network had given Mr. Trump too much airtime when the network aired Mr. Trump’s live news conference last week after his civil fraud trial. Mr. Murphy said that CNN should cover Mr. Trump’s comments when he makes news, not when he is repeating political talking points.

The debate on the conference call, which was open to thousands of CNN journalists, was described by three people who either listened to the call or were briefed on its contents. They requested anonymity to avoid reprisal for sharing details of a conversation intended to be private.

The exchange between Mr. Thompson and Mr. Murphy, which lasted about 15 minutes, was lively but collegial, the people said. According to one account, Mr. Thompson said he believed that CNN had struck the right balance between allowing the public to hear from the Republican front-runner, while not allowing Mr. Trump an endless soapbox — and that he believed that CNN, at some points during the 2016 election, had granted Mr. Trump too much airtime. It is a criticism that the network’s president at the time, Jeff Zucker, has acknowledged.

The conundrum of covering Mr. Trump, who often rapidly unleashes incendiary and misleading remarks, has vexed news executives since the earliest days of his first presidential run. The tensions within CNN speak to continuing debates in journalistic circles even as Mr. Trump moves closer to clinching the Republican nomination.

On MSNBC, a network popular with left-leaning viewers, the anchor Rachel Maddow told viewers on the night of the caucuses that she simply would not broadcast Mr. Trump live.

“It is not out of spite. It is not a decision that we relish,” Ms. Maddow said. “It is a decision that we regularly revisit, and honestly, earnestly. It is not an easy decision. But there is a cost to us as a news organization of knowingly broadcasting untrue things.”

That approach earned mockery from a Trump ally, the Fox News anchor Sean Hannity, later in the week. “What?” Mr. Hannity said on his Fox News program. “The audience is going to melt if they hear him?”