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Donald J. Trump again turned his Twitter vitriol toward an old foe this week: Megyn Kelly, the Fox News anchor and frequent target of his social media ire. On Friday, the network said it had had enough.

Mr. Trump’s attacks on Ms. Kelly date to August, when she asked him at a debate about his history of disparaging remarks toward women. Afterward he called the questioning unfair and suggested that Ms. Kelly had been menstruating. After Fox News declined his request to remove her from the moderating panel for the network’s January debate in Iowa, Mr. Trump skipped it.

Détente seemed to have been reached when Mr. Trump appeared at the Fox News debate, with Ms. Kelly moderating, earlier this month. The two had a cordial interaction.

But Mr. Trump resumed his sniping at Ms. Kelly on Tuesday, apparently feeling that she had understated his success in the Republican presidential primaries.

Can't watch Crazy Megyn anymore. Talks about me at 43% but never mentions that there are four people in race. With two people, big & over! — Donald J. Trump (@realDonaldTrump) March 16, 2016

Everybody should boycott the @megynkelly show. Never worth watching. Always a hit on Trump! She is sick, & the most overrated person on tv. — Donald J. Trump (@realDonaldTrump) March 18, 2016

On Friday night, after Mr. Trump called for a boycott of Ms. Kelly’s show, the network responded through a spokeswoman.

“Donald Trump’s vitriolic attacks against Megyn Kelly and his extreme, sick obsession with her is beneath the dignity of a presidential candidate who wants to occupy the highest office in the land,” said Irena Briganti, a spokeswoman for the network. “Megyn is an exemplary journalist and one of the leading anchors in America — we’re extremely proud of her phenomenal work and continue to fully support her throughout every day of Trump’s endless barrage of crude and sexist verbal assaults. As the mother of three young children, with a successful law career and the second highest rated show in cable news, it’s especially deplorable for her to be repeatedly abused just for doing her job.”

Ms. Kelly, as she had in the past, has stayed out of the crossfire, opting not to respond personally to Mr. Trump’s provocations.

Later Friday night, the Trump campaign responded in a statement from its spokeswoman, Hope Hicks:

“Megyn Kelly is a highly overrated reporter and anchor that constantly disparages Mr. Trump with negative and inaccurate reports. Despite the fact he wants nothing to do with her and will not appear on her show due to her extremely biased reporting, much of the program is about him anyway on a nightly basis.”

“Unlike Megyn Kelly, who resorts to putting out statements via FOX News, Mr. Trump will continue to defend himself against the inordinate amount of unfair and inaccurate coverage he receives on her second-rate show each night.”