He however referred to recent allegations from other countries, alleging incidents of hacking into government networks by Chinese spies.
"What I can stress is that absolutely no classified information has ever been penetrated by these attacks"
Helen Clark, New Zealand prime minister
Tucker said some departments were unaware of the security breach, which resulted in attempts to access classified data.
He said a programme was installed in one attack to generate bogus but genuine looking e-mails.
Following Tucker's revelation, Clark moved to quell concerns that foreign spies had made off with secret data.
"The assurance I've been given by intelligence agencies is that no classified information has been at risk at all," she said.
"What I can stress is that absolutely no classified information has ever been penetrated by these attacks."
Clark also said she knew which governments were involved but declined to name them, saying the issue had not been taken up with the countries concerned.
"That's not the way intelligence matters are handled," she said. "It's not something unique to us, it's something that every country is experiencing."
Last week, China was accused of hacking into German and US government computer systems, including networks at the Pentagon.
In the latter case, officials quoted by the Financial Times said the alleged Chinese hack was the most successful yet on US department of defence computer networks.
China has denied its agents were involved in any of the hacks, describing such allegations as being the product of a "Cold War mentality".
Russia and China have also been implicated in cyber-espionage attacks on the British government's computer network, including the websites of the UK foreign ministry and the House of Commons, the lower house of the British parliament.