After the firing, the network commissioned an inquiry overseen by NBCUniversal’s general counsel, Kimberley D. Harris. It led to a report clearing NBC News management of wrongdoing. Other media organizations that have dealt with accusations of workplace misconduct, including Fox News, CBS and NPR, hired outside law firms to conduct similar investigations.

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Mr. Farrow also accuses the NBC News president, Noah Oppenheim, of smothering an investigation into the movie mogul Harvey Weinstein, which Mr. Farrow later published to acclaim in The New Yorker. NBC has said that, at the time, Mr. Farrow’s reporting fell short of NBC standards and that the network was “profoundly disappointed” not to have aired his eventual findings.

The candidates’ letter, first reported by HuffPost, seems to embrace Mr. Farrow’s reporting and analysis. “It is critical that the Democratic National Committee make clear that they support survivors of sexual harassment and abuse by ensuring that Comcast and NBC News take steps to clean up the toxic culture that exists across their networks,” the letter reads.

The letter also asserts , without evidence, that network managers covered up incidents of abuse. Last month , Andrew Lack, the chairman of NBC News, sent a memo to the staff, saying that “any suggestion” that NBC News executives had known about Mr. Lauer’s behavior before the accusation or tried to cover it up “is absolutely false and offensive.”

The Democratic National Committee has no direct way to ensure that Comcast takes any action. UltraViolet’s executive director, Shaunna Thomas, who has organized protests outside NBC’s Manhattan headquarters, said in a statement on Tuesday that Democratic officials have “leverage as a critical media partner in the 2020 election” to “push Comcast and NBC to do the right thing.”

The Democratic National Committee said on Tuesday that it had not received a formal copy of the letter and had no further comment. Comcast did not respond to a request for comment on Tuesday.

NBCUniversal referred to its previous statements that the news division was confident in the results of its internal review, and that network executives had taken swift and appropriate action to address accusations of misconduct.