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Curran, who last week resigned as a minister citing intolerable pressure following her sacking from the Cabinet, earlier released correspondence from her Gmail account between her and Handley over the secret meeting she held with him, which ultimately led to her demotion.
Today, while responding to reporters' questions over whether she had released all the emails relating to her dealings with Handley, Curran admitted there may be more.
"They are the full chain of emails that related to the meeting that I had with him in February. There may be some more."
Curran declined to say what the subject of those emails was.
"As I've said, I've given an assurance to the Prime Minister that I'm archiving my emails, and that's what I'm doing. I'm going through a process to do it and I haven't completed that process yet."
Curran was stripped of her open government and government digital services responsibilities after failing to disclose the February meeting.
The meeting was over his interest in the vacant government chief technology officer role. It was held at 8pm in Curran's Beehive office with nobody else present, and was not put in her diary.
The next month Curran responded to a written question from National but failed to disclose the meeting.
The meeting was one of two Curran failed to disclose. The other was a cafe meeting with former RNZ head of content Carol Hirschfeld in December last year.
The fallout from the pair's failure to disclose the meeting resulted in Hirschfeld losing her job.
National's broadcasting spokeswoman Melissa Lee said she did not have confidence that Curran would release all her Gmails that relate to government business.
"She is deciding what is relevant and what is not but she's no longer a minister, so I'm a little bit concerned that we may not get to the bottom of it."
Lee said Curran should give her Gmail password to someone else who could go through her Gmails to look for relevant emails.
Meanwhile, rookie Labour MP Greg O'Connor said he got it wrong when he told Newstalk ZB yesterday that Ardern's handling of Curran's decision to resign on Friday "could have been done better".
O'Connor received a "stern phone call" from Ardern after his criticism that there was confusion over the Prime Minister's media interviews ahead of the public announcement of Curran's resignation.
O'Connor also said Curran had been sacked when in fact she resigned.
Today he told reporters he got it wrong.
"I've apologised and I've got the message. I got it wrong, my understanding of the events. It was fair to say the Prime Minister wasn't happy. I wouldn't have been happy either. So yes, I got a telling off."
Ardern said today O'Connor had said something he shouldn't have and had apologised unreservedly.
"I am happy to take feedback directly from my colleagues. I expect it directly," Ardern said.