Fox News on Wednesday urged a federal court to discipline a lawyer it said had failed to vet basic facts when he filed a lawsuit accusing the network of using fake Twitter accounts to harass a former host.

In a court filing, lawyers representing Fox and two of the network’s top executives accused the lawyer, Judd Burstein, of making “outrageously and flagrantly” false claims on behalf of his client, the former Fox News host Andrea Tantaros.

Ms. Tantaros has said that Twitter posts from so-called sock-puppet accounts were part of a concerted effort to silence her after she complained about sexual harassment by Roger E. Ailes, a network founder who resigned as chairman and chief executive last summer. Mr. Ailes died this month.

Judd Burstein, a lawyer for the former Fox News host Andrea Tantaros.

In the filing, Fox said Mr. Burstein had failed to do basic research into one of the accounts he cited, which posted under the name Daniel Wayne Block. “One phone call would have proven that Mr. Block is alive and well and has no connection to Fox News, other than as a fan,” the filing said.

Fox also said Ms. Tantaros’s claims that several of Mr. Block’s Twitter posts showed that the network was eavesdropping on her calls could easily be disproved by his posting history.

“Mr. Block often sent the same or similar purportedly threatening images before the allegedly monitored telephone calls,” the filing said, citing several examples.

Mr. Burstein called the filing “frivolous” and said the contradictions contained within inadvertently demonstrated the network’s guilt.

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“Fox News has now handed me the smoking gun — evidence that they were electronically surveilling Ms. Tantaros’s telephone conversations,” he said in a statement.

For example, he said, a critical post by Mr. Block was removed as Mr. Burstein prepared to cite it in the lawsuit, suggesting that his or Ms. Tantaros’s communications were monitored. And Mr. Block’s statement that he was “not familiar” with a Twitter account with which he exchanged messages called into question whether someone else was responsible for some of his posts, Mr. Burstein added.

“Plainly, there was a slip-up between Fox News and its lawyers, which caused this unwitting self-immolation,” he said in a statement.

Fox News argued, though, that this case demonstrated a “dereliction of a lawyer’s most basic responsibilities.”

The network has asked that Ms. Tantaros’s claims be dismissed and that Mr. Burstein be disciplined, and that she and Mr. Burstein pay Fox News for its legal costs.