Foreign Affairs Minister Murray McCully says it was up to his staff which email accounts they used to send him official correspondence.
Hackers got into Mr McCully's private email last April. It was an account to which some of his official emails had been forwarded.
In a statement, Mr McCully says the email account was used by his office to send media items and office administration material to him.
He says any Cabinet material and diplomatic cables were sent through a secure system.
However, the incident has prompted a warning from Prime Minister John Key for ministers to be more careful with online correspondence and passwords.
Clear breach - Peters
New Zealand First leader and a former foreign minister says forwarding official emails to a private account is a clear breach of protocol.
Mr Peters says forwarding any official correspondence to a private account is unacceptable.
Telecom would not comment on whether other email accounts had been hacked and would not say if its security systems were under review.
However, a spokesperson says Xtra has extremely extensive security measures which are updated regularly.
The Dominion Post reports the Anonymous group broke into Murray McCully's private Telecom email account.
A spokesperson for the Prime Minister confirms the breach occurred last April, but says Mr McCully's ministerial email was not involved.
However, he did have official emails forwarded to his private address.
The spokesperson says that does not appear to have broken any protocols.
Labour communications spokesperson Clare Curran says it appears the hackers were protesting about copyright law reforms.