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It follows yesterday's release of email correspondence between the two parties, showing National's general manager Greg Hamilton acknowledging a National Party staff member was responsible for exploiting a security vulnerability to access confidential donor and member information from Labour's databases in 2011.
"We do accept that one of our staff visited your public website ... and read files that were publicly available," the email reads.
Labour leader David Cunliffe demanded an apology from Mr Key yesterday, saying the email proved he had been "misleading" the public over the allegation, raised in author Nicky Hager's new book, Dirty Politics.
This morning Labour's campaign spokeswoman Annette King said Mr Key should now reveal who that staff member was, "because all the evidence points to [Key's close advisor] Jason Ede".
"New Zealanders deserve better. They want answers. Dirty Politics makes it clear that Jason Ede claims to have accessed the website but John Key can't make up his mind who Mr Ede works for," she said.
"Mr Key and National must name the staff member who accessed Labour's website to clear up this matter once and for all."
Revealing the email yesterday, Mr Cunliffe would not name the person he alleged accessed Labour's website, saying "you can draw your own conclusion".
"It's clear from Mr Hager's book, he [Mr Ede] seems to be John Key's main point man on those kind of operations," he added.
However, National hit back yesterday accusing Labour of digging up "old news" in a bid to smear the Government.
"As Mr Hager's claims continue to disintegrate, Mr Cunliffe has tried to help him out, releasing an email which confirms only what the National Party stated openly at the time - that a National IT staffer accessed publicly available information on Labour's website which the Labour Party had not properly secured," said campaign chairman Steven Joyce.
"The National Party was open with the Labour Party, the public, and the media about this back in 2011."
- Patrice Dougan of APNZ