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He said Handley had been treated "shabbily" after being appointed to the job of chief technology officer by former Digital Services Minister Clare Curran then having been dumped by new minister Megan Woods.
He said the text and email correspondence released by Handley clearly showed Ardern and Handley were mates at some level - although there was nothing to suggest he had got the job because of that.
Handley has released all his texts and email correspondence with Curran and Ardern in a bid to show there was nothing untoward in them.
But Bridges has zero-ed in on answers Ardern gave to him in Parliament a week ago in which she mentions only one text, and denies engaging with Handley on the issue of the CTO job.
The messages from Handley show three text from her to him and six texts from him to her.
As stated, Ardern does not engage with him on the issue of the CTO job but she gives him her private Gmail address after he texts her saying: "A number of people have urged me to seriously consider this CTO thing ….I think that role is more about society than technology so I'm not sure the average CIO [chief information officer] or CTO is the answer," and the following day he asks for the best email address to send some "starter thoughts."
He emails her with a longer message including some ideas to help her, which he said he wanted to do whether or not he got the job of CTO. In one of his texts he asks: "PS how's mumhood?"
Bridges told reporters at Parliament today that Ardern had "misled the Parliament and she has misled the public."
"She has presented a picture of one text of a very cursory sort of a thing when actually it is much more than that.
"It is clearly to her as Prime Minister and they are clearly discussing what could be for Derek Handley should he or when he comes back. It is a very misleading picture she has presented in Parliament vs the facts.
"I say to the Prime Minister, you should correct Prime Minister. That is the right thing to do. That is what parliamentarians have always done on issues like this."
Bridges said it was important to see everything, including the correspondence between Ardern and Curran.
"It seems clear to me there are more texts, emails, correspondence to work out what has happened for a Government claiming to be open and transparent but sadly is looking anything but."
Ardern said in New York this morning that she nothing to correct in Parliament, a view backed up by Acting Prime Minister Winston Peters, Finance Minister Grants Robertson and deputy Labour leader Kelvin Davis.
Last Tuesday she said: "I can rule out any direct verbal communication. I haven't spoken with Mr Handley in at least a year, maybe two. As I say my best recollection is I received a text message that I didn't directly engage in. For all other platforms, I would want to go back and check, but I don't recall directly communicating in regards to that role."
Robertson forced to correct answer in Parliament
Grant Robertson has been forced to correct an answer he gave Parliament last week after advice from Curran led him to not fully disclose her email exchanges with Handley.
After requests from National's Nick Smith last week and a direction from Speaker Trevor Mallard to bring Curran's email exchanges with Handley to the debating chamber, Robertson last Wednesday outlined the dates and content of each email between Curran and Handley during the recruitment process for the Government's chief technology role.
But the release today from Handley of all communications between him and Curran, and the Prime Minister showed that three emails were missing from the list Robertson read out last week.
Today Robertson said that in an answer to an oral question on September 19, he inadvertently left out three emails between Curran and Handley.
"I was unaware at the time of giving the answer that there were two further emails on 11 August from Clare Curran in response to Mr Handley's original email and an email from Mr Handley on the 13th of August to begin the process for setting up a phone call.
"I apologise to the House for that," Robertson said.
A spokesman for Robertson said he had been acting on the advice of the former minister when he gave his original answer in Parliament.
Comment is being sought from Curran.
The three emails in question are responses from Curran to Handley in response to his email of August 11 with questions and thoughts on the CTO role.
Among the queries Handley has are potential conflicts of interest.
In the one of the newly released emails, Curran replies: "Good thoughts. I think the [redacted] one is a biggie. Will talk through that with a few people. The other potential conflicts don't leap out at me though Cabinet Office will have a view."
The email goes on to discuss announcing his appointment and resourcing, before suggesting times they should talk.
Handley then sends another email asking about timing for their talk.
In a statement, Smith called the situation a "fiasco".
"Ministers are just compounding the mess over the CTO role with error upon error. Grant Robertson had to admit with a personal explanation to the House this afternoon that despite weeks of questions and a specific instruction from the Speaker that the Government last week failed to disclose all of the relevant emails from former Minister Clare Curran," said Smith, National's State Service spokesman.
"This came on top of the Prime Minister claiming she's only had one text from Mr Handley that she did not respond to. Mr Handley's disclosures today show both ministers were being economical with the truth at best.
"It was also a mistake for Megan Woods to not have personally communicated with Derek Handley when she cancelled his job on 14th September without warning, particularly when ministers had engaged in dozens of communications with him up until that date," Smith said.
He also took issue with Woods' error this morning when she said there was a confidentiality agreement as part of Handley's settlement. Woods said later that she had received incorrect information from officials and there was no confidentiality agreement associated with Handley's settlement.
Simon Bridges said he imagined Handley would be feeling "pretty rotten" about the matter for him to release his correspondence.
"He is obviously at some level a mate with the Prime Minister and that is there but the truth is he has been treated shabbily."
"He has had a series of texts and communications with the Prime Minister and the minister. He has been offered the job, he has packed up his family, he has come back to New Zealand and then he has been unceremoniously dumped. And he has had no explanation for that.
Bridges said there was nothing to suggest that Handley got the job because he was friendly with the Prime Minister.
"But it did give him the in. It did mean he did have the cellphone number of the Prime Minister. It did mean that she gave him her private Gmail…It did mean they were going to catch up in Titirangi down the track. The truth is, I suspect, we will never know in fact what the Prime Minister to Clare Curran about this, whether she said 'look this is my mate, this is a great person, he should be in the role, he is the guy for the job.'"
He said the Government was shoddy at declaring mateships and friendships and such relationships should be declared.
He disputed whether Ardern had declared her knowledge of Handley but in fact Hansard shows she told Parliament last Tuesday she had done so at cabinet's appointments and honours committee where he had been appointed.
- By Audrey Young and Lucy Bennett