Fox News on Tuesday retracted a story linking the murder of a Democratic National Committee staff member with the email hacks that aided President Trump’s campaign, effectively quashing a conspiracy theory that had taken hold across the right-wing news media.

It was a rare acknowledgment of error by the network. But it also underscored a schism between the network’s news-gathering operation and one of its biggest stars: the conservative commentator Sean Hannity, who has unapologetically promoted the theory and remained defiant on Tuesday.

“These are questions that I have a moral obligation to ask,” Mr. Hannity said on his radio show, shortly after Fox News announced its mistake. “All you in the liberal media — I am not Fox.com or FoxNews.com. I retracted nothing.”

The story of the murdered aide, Seth Conrad Rich, who was 27 when he was shot in the back near his Washington home in July, has been seized on by Mr. Hannity and other right-wing pundits as an alternative narrative to the cascade of damaging revelations about the Trump administration’s ties to Russian officials who meddled in the presidential election.