His comments come after New Zealand First leader Winston Peters called for an "immediate inquiry" into the decision to grant Mr Dotcom - previous Kim Schmitz - residency.
The native German was granted residency in 2010 under the "high-investment category", after putting $10 million into government bonds and making a large donation to the Christchurch earthquake fund.
However Mr Peters said it is hard to understand how Mr Dotcom passed the "good character" requirements for New Zealand residency, given he had previous convictions.
Mr Dotcom told the Herald on Sunday last year he was convicted for "hacking" under juvenile law and for insider trading because of ignorance about a share-trading law. Both convictions were more than 10 years ago and had been wiped by Germany's clean-slate law, he said.
"The prime minister should order an immediate inquiry by a qualified person to see who was involved in this immigration scandal and ensure that it doesn't happen again," Mr Peters said.
"He had a clean slate because those convictions happened many years earlier under German law, so the New Zealand officials contacted the German police, they confirmed that I guess on the balance they decided to let him in without reference to the ministers," he told Newstalk ZB's Susan Wood.
Mr Key said the fact that he declared them, meant he passed the test of good character.
"I think because they deemed under the clean slate legislation he effectively didn't have a record and he wasn't trying to hide anything, those convictions were a long time ago, so they let him through," he said.
Mr Key said this case does not necessarily mean the law needs to be changed.
Dotcom and three others appear again in the North Shore District Court today, fighting a bid by the FBI to extradite them.
Acknowledgements and thanks - Newstalk ZB, Herald Online