The Government says the National Party is not telling the public what it really plans to do with Kiwibank.
Three News has played a recording of a private conversation in which National's deputy leader, Bill English, said the party would eventually sell the bank.
The party has pledged that it will not sell public assets during a first term in office.
Finance Minister Michael Cullen says National has promised unaffordable tax cuts, and may fund them through the sale of public assets.
He says Kiwibank has helped to keep down banking fees by competing with its foreign-owned rivals, it would probably fall into the hands of a big, Australian-owned bank if it was sold.
Mr English says the recording does not contradict National's position, that it would only sell public assets after a first term in power if it had a mandate from voters.
"In fact, the bit that TV3 didn't play has me saying that while some of our supporters worry about Kiwibank, it's actually working.
"So no, there's no issues of public trust, our position's quite clear."
No change to policy - Key
National Party leader John Key told Morning Report on Monday there is no contradiction in the statement, as National has made it clear it would not be selling any assets in its first term.
"If there's any change to that position - and we're not working on that - but if there's any change to that position we will go out with a mandate, we will go out to seek that mandate by going out and asking the voters of New Zealand whether they support a particular policy or not."
Mr Key said the last serious discussion the Party caucus had about Kiwibank was before the 2005 election, when it supported keeping the bank.
Progressive Party leader Jim Anderton led the drive to establish Kiwibank. He says the bank provides competition for overseas-owned banks, keeping fees and interest rates lower.
Mr Anderton says Kiwibank has kept its competitors honest, but that would change if it fell into foreign hands.