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Mr Hipkins addressed National's handing of sensitive patient information at today's Covid-19 briefing after it was revealed Woodhouse was also leaked private details about Covid-19 patients by former president Michelle Boag.
National leader Todd Muller has said he believes his party has been "transparent" about the leak of Covid patient details.
He has rejected it was a lie by omission that he didn't reveal Woodhouse also was sent sensitive information by Boag.
"From my perspective, we have been well-managed and transparent about it."
Meanwhile, Woodhouse said he didn't say something sooner because he didn't think he had the same information as Hamish Walker, who admitted leaking details of 18 active Covid cases to media.
Asked if Muller was lying, Hipkins said: "That's a matter for Todd Muller and for the National Party.
"It is clear however, that over the course of the last week the National Party have had a lot of information they have chosen not to share that could have cleared things up much more quickly."
Muller and Woodhouse had made some "very strong comments" about the leaked information over the weekend when it was clear they knew how it came to be released, Hipkins said.
"Our focus is on responding to Covid-19, it is on doing everything we can to keep New Zealander's safe.
"Issues like this distract a lot of time and energy and focus away from that response."
He said when Labour was in opposition it had in some cases informed the National government, including one case involving Dunedin MP Clare Curran, about privacy breaches before going public.
Ms Curran became aware of a vulnerability in an IT system that meant people's details were available.
"She reported that to the government, gave the government an opportunity to fix it and then after that was done went public with the information.
"It's absolutely legitimate to call out if there has been a failure of information handling.
"It is not legitimate to release that information or to sit on that information and not do anything about it."
The comments come after Curran was critical of Woodhouse for him posing with a blue toilet seat with her face emblazoned on it back in 2012 - a photograph she said traumatised her.
Mr Woodhouse, who was standing at Mr Muller’s side, did not say if he regretted the incident when questioned earlier this week.
He said he had made no public or social media comment on the incident in eight years "and I don’t intend to do so now".