It comes after Ms Dorries shared a video on social media suggesting Sir Keir had been reluctant to prosecute grooming gangs when he was director of public prosecutions.
The MP for Mid Bedfordshire re-tweeted the clip of an interview with the new Labour leader in which he appeared to be listing a series of reasons for not bringing charges - including if the alleged victims had been in trouble with the police - with the comment "revealing".
But Labour said the video had clearly been "doctored" and that he was actually responding to a question from the interviewer about the flaws in previous guidance to prosecutors which he had withdrawn and replaced.
In response to the post by Ms Dorries Labour's Wes Streeting replied:
"What’s revealing is that: 1. You’ve spread fake news and indulged a smear being promoted by the far right. 2. You had time to do this despite being a minister in the Department of Health during a public health crisis."
"It’s either malevolence or stupidity. Probably both."
The former senior prosecutor Nazir Afzal - who was involved in bringing a number of cases - said the clip was being used to suggest Sir Keir did not take child sexual abuse seriously, when the opposite was true.
"As national lead, I can assure you that he and I put right the failings of a generation of those who should have safeguarded children.
"He inherited failure and left success," Mr Afzal tweeted.
A Labour Party source said: "This is a doctored video tweeted by a far-right social media account.
"As a government minister, we hope Nadine Dorries acknowledges this and takes it down."
Following the furore - the posting appeared to have been deleted from Ms Dorries's timeline.