Liberal Leader Justin Trudeau says he will "continue to not engage" with Sun Media – one of the country's largest newspaper and media organizations – after one of its columnists and TV hosts made critical and personal remarks about Mr. Trudeau's parents.

The five-minute segment from Ezra Levant, aired last Monday, took aim at former Prime Minister Pierre Trudeau and Margaret Trudeau. Mr. Levant spoke at length about the "conquests" of the two and called the former Prime Minister "a slut."

Justin Trudeau's office released a statement Tuesday saying Mr. Levant's segment "crossed the line by airing a personal attack on the Trudeau family that was offensive and breached any reasonable measure of editorial integrity." The statement said he had "raised this issue with the appropriate people at Québécor Inc.," the parent company of Sun News. Until Québécor "resolves the matter," Mr. Trudeau said he personally will "not engage with Sun Media."

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The practical effect of the move is unclear. A spokeswoman for Mr. Trudeau said the threat to "not engage" applies to all of Sun Media – that includes the Sun News television station, which is fiercely critical of Mr. Trudeau and the Liberals, but also 36 paid-circulation daily newspapers and almost 200 community newspapers. Many of the chain's papers aren't part of the Sun brand, but the Liberal statement did not discern between them – raising the prospect of the entire chain being frozen out.

Mr. Levant and other Sun employees said Tuesday that Mr. Trudeau has already been avoiding them. "It's useful for Trudeau to blame a commentary I did in 2014 for why he didn't answer our questions in 2013, 2012, etc.," Mr. Levant wrote in an email.

He said Mr. Trudeau is trying to censor him by pressuring Quebecor.

"There are two separate issues here. The first is: do people agree with my political commentary? It's not surprising that the Liberals don't. It's called freedom of speech. The second is: was it appropriate for Trudeau to contact Quebecor and demand that I be censored? And, when Quebecor did not accede to that demand, that Trudeau then engages in mass punishment of every Sun journalist?" Mr. Levant wrote in an e-mail.

A key figure of Mr. Trudeau's inner circle, Gerald Butts, pointed to several graphics produced by Sun News, the network, critical of Mr. Trudeau and the Liberals. "Is there a line, and has Sun crossed it? We believe the answer to both questions is yes," Mr. Butts wrote on Twitter, adding that reporters from "real journalistic outlet[s]" won't face reduced access.

Mr. Levant's segment was sparked by a photo, published on Twitter by a Liberal official earlier this month, that showed Mr. Trudeau kissing the cheek of an unidentified bride. Mr. Trudeau was said to be leaving a party event when he stumbled across the bride, who appeared to be shooting photographs with her wedding party. He kissed her on the cheek.

In his segment, Mr. Levant criticized Mr. Trudeau for kissing the bride as well as the media's coverage of Mr. Trudeau. He then discussed the "conquests" of Mr. Trudeau's parents, saying they were "promiscuous and publicized how many conquests they had." He said Pierre Trudeau was "a slut," listing some of his previous partners, and that Margaret Trudeau "tended toward rock musicians." Mr. Levant then added: "Now, if that's your moral compass, kissing another man's bride on her wedding day is pretty cool." He published a similar column a week later. While it didn't use the word "slut," Mr. Levant said on Tuesday he doesn't regret the word choice. "I do stand by calling Pierre Trudeau a slut, though. I don't believe in double standards, e.g. men are virile, women are sluts," he wrote on Twitter.

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Speaking to reporters after question period, Mr. Trudeau declined to detail the move, saying the written statement released by his office was clear.