On their website, Mr. Dick and Ms. Ziering dismiss critics of the film, saying, “The truth is on our side.” In a statement on Sunday afternoon, they said: “We were not surprised by the lengths Mr. Winston and his lawyer were willing to go to stop the public from seeing this film. When documentaries bring to light uncomfortable truths about powerful people and institutions, it’s not unusual for them to wage aggressive campaigns to silence their critics. We fully stand behind Erica Kinsman and all of the survivors who bravely spoke out in our film.” Ms. Kinsman is Mr. Winston’s accuser.

Mr. Winston’s threat of legal action came a week after 19 Harvard professors attacked “The Hunting Ground,” saying it distorted the university’s handling of a sexual assault claim. The accusation eventually resulted in a conviction for misdemeanor nonsexual assault against a student, Brandon Winston, who was not named in the film, but was named in the professors’ letter. Late last week, Brandon Winston’s defense team and supporters unveiled an elaborate website that explains their view of his actions and takes “The Hunting Ground” to task for what it calls “critical omissions and distortions.”

Mr. Dick and Ms. Ziering last week challenged the Harvard professors’ action in a text message to The New York Times. It said, in part: “Everything in ‘The Hunting Ground’ is accurate and we fully stand behind our Harvard Law survivor’s account of her assault, as well as the accounts of all the subjects in our film.”

Escalating denunciation of “The Hunting Ground” comes as the movie is being considered by members of the Academy of Motion Picture Arts and Sciences for a so-called short list of 15 documentary feature Oscar contenders, which will be released next month. The film’s critics have also had an eye on the large viewership CNN may bring to a film that found only a tiny audience in theaters when released in February by the Weinstein Company’s digitally oriented Radius-TWC unit.

As of March, for instance, another controversial documentary, “Blackfish,” about the treatment of whales in captivity, had been seen by about 27 million viewers on CNN, though it had just $2 million in ticket sales when Magnolia Pictures released it in 2013.