National leader Simon Bridges, who also received the text, has suggested Mallard was influenced by Ardern's public comments when she said it was an internal matter for National and should be dealt with sensitively.
Shadow leader of the House Gerry Brownlee said today there had been no need for Mallard to advise the Prime Minister of his decision to cancel the inquiry.
"On what basis did he do that?"
Mallard had said he believed the leak came from National and the Prime Minister had said it should be dealt with sensitively, said Brownlee.
"On what basis do they make that statement? Do they know? And are they simply not telling us because of some commitments around parliamentary security and diplomatic protection security."
Brownlee said the information included in the anonymous text message which tried to establish the person's bona fides as a National MP could have been picked up by gossip or by hacking.
The content of the text message was not conclusive proof that the person was a National MP.
RNZ revealed at 6 am on Friday that the text had been sent the week before, Bridges had a standup at about 9.30 am and revealed he had referred the text to the police, Ardern made her comments about the National Party at about 10 am, Mallard spoke to Simon Bridges at 11.30 am, Mallard spoke to the Prime Minister at 11.45 am, and he issued his statement cancelling the inquiry about 12.45 pm.
Brownlee said if Mallard knew who the person was who leaked the document and sent the texts, he should tell National.
"He has made it very clear that his concerns are about the well-being of the individual concerned and we would share that concern and want to do something about it."
Brownlee did not believe there would resistance among the caucus to National conducting its own investigation about the leak with a forensic specialist.
"Most MPs are pretty incensed that the Speaker has gone out and effectively pointed the finger at our caucus and made a couple of pretty serious accusations – one of extreme disloyalty and another of a problematic mental illness."
Brownlee said the inquiry would be a private matter and National would not be commenting on the methodology.
He said the leak had been more of an "irritation" than a distraction.
But the security of the parliamentary communications system was still a significant worry particularly over the next two years when the party would be engaged in policy formation.
Mallard has been asked for comment but he is on holiday abroad and after cancelling the inquiry on Friday said he would not be commenting further.
The Police have declined to say whether they have made further contact with the texter after identifying them more than two weeks ago or whether the person is connected to National.
"We reiterate our comment from Friday that Police will not be disclosing any information about the identity of the individual for privacy reasons," a spokeswoman said.
"We also reiterate that Police assessed the information supplied [by Simon Bridges about the text] as a mental health issue requiring an immediate response.
"It is not subject to other investigative steps. We are not going to discuss any matters regarding specific steps taken regarding the welfare of the individual. "
