"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.
Mr Key defended the decision to allow Mr Dotcom into the country.
"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.
- Newstalk ZB, Herald Online