The letter claimed the video showed "a false and misleading account of proceedings".
"Mr McAnulty's letter has highlighted the existence of a range of videos posted by different parties that use footage of members for political advertising.
"I would be very surprised if those members had given permission, as the rules currently require."
Last week National posted a video featuring Russell that showed her making a speech about wellbeing, but trailing off-topic and onto Greek philosophy.
Before the video, text read: "Still not sure what Labour's Wellbeing Budget means?"
"While there has been some discussion about what constitutes a 'political advertisement', it is clear to me that videos that support one party or to aim to reduce support for another party are the sorts of items covered by [Parliament's rules]," Mallard said.
"That view is further reinforced by the description of the video as an "attack ad" in the material [National Leader Simon] Bridges referred me to."
He later clarified the ruling only applied to videos posted this year.
According to Parliament's rules, footage from the House – by Parliament TV – is not allowed to be used for political advertising or election campaigning - except with the permission of all members shown.
It also states reports that use extracts of coverage of proceedings and purport to be summaries must be fair and accurate.
If an MP uses footage from the house in ads without the permission of the MP it features, they will face contempt – a serious offence in Parliament.
Mallard asked Opposition leader Simon Bridges and his office to "refrain from editing official video footage of MPs and posting it".
Bridges on Thursday called the decision an "attempt at stopping the Opposition from highlighting what goes on in Parliament is a chilling move designed to stop freedom of expression".
"Sound bites have been used this way for decades in all forms of media and by all New Zealand political parties," he said.
"National believes it is important for New Zealanders to see how their elected representatives perform in Parliament."
Bridges rejected the video of Russell was false or misleading.
"The video did not attack or criticise the Labour Party or the Government. It accurately reflects Dr Russell's speech to Parliament about the meaning of 'wellbeing'," he said.
"When National was in Government, Labour also used footage from Parliament. Often heavily edited. We didn't complain as we stood by our record and we encourage political debate."
Speaking to media after Question Time, Leader of the House Chris Hipkins said the rules around video in the House were clear.
"The National Party's current use of video footage of Parliament does breach those rules."
He said MPs shouldn't have their quotes in the House clipped and portrayed in a way that is used for political attack.
Deputy National leader Paula Bennett said Mallard's ruling was "censorship at the extreme" and said the ruling would affect hundreds of Labour, Greens and National ads.
It would affect NZ First couldn't "they can't master technology", she said.
