He also ordered National leader Simon Bridges and his office to stop posting any new footage of MPs until the Standing Orders Committee had considered the current rules.
Bridges defied the order and the offending material was reposted by all National MPs but they complied after a week.
The standing orders committee, which oversees Parliament's rules, held an urgent review into the rules of Parliament TV (PTV).
The report of the Standing Orders Committee chaired by Mallard says: "We do not believe that members featured in PTV coverage should have the right to veto political advertising in which they are shown.
"Members speaking in the House are in a public place, making public comments, and it is right that they be held to account for what they say or do when speaking."
The report says that the rules should seek to prevent parliamentary TV coverage from being used in a misleading way but it wants to look more closely at the wording of the rules.
But it says the Speaker should get extra powers to direct anyone breaching the conditions of use to stop using the coverage or altered in a way to bring it into compliance.
But it also recommends that the privileges committee should be given the authority to review such direction by the Speaker - to begin within two working days after the Speaker's order - and to accept it or recommend it be revoked.
The committee's new recommended rules are going to be introduced on a trial basis through a new sessional order being published, the report says.
Sessional orders expire at the end of the parliamentary session.
The rules wont just apply to MPs. If a member of the public posts a misleading ad using Parliament TV, the Speaker could ask for it to be taken down or changed.
If his directions are ignored, that person who produced the ad could be called to appear before the privileges committee.
