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Despite the fact the ad was authorised by National leader Judith Collins, Mallard said she has assured him that she did not see it before it was published.
Mallard said it was National's general manager, Greg Hamilton, who was responsible for the post.
Nevertheless, Collins has apologised and assured the Speaker that the material would not be put back on social media.
The ad included the text of a written question National's health spokesman Shane Reti had asked Health Minister Chris Hipkins.
It had a fake ministerial letterhead as well as the Labour Party's logo.
This, according to Mallard, was meant to "lend authenticity to the misrepresentation".
The Privileges Committee acts as the rulekeeper of Parliament and MPs are sent there if they go against the rules in a significant way.
However, since Collins apologised for the ad and has taken it down, Mallard said he does not intend to take any further action.
It was Hipkins who complained about the ad – he said it was an "alteration and misrepresentation of a reply to a written question," Mallard said.
This is not the first time National has been in hot water over its advertising.
In February, National lost an appeal to the Advertising Standards Authority over a Facebook ad they were forced to take down.
That was in relation to an ad criticising the Government's proposed clean vehicle feebate scheme.