Both victims remain in hospital.
Two women from the alleged offender's family were in court for the appearance.
He appeared wearing a police-issued kevlar vest and responded quietly when asked to confirm his name.
He sat quietly during the hearing before Justice of the Peace Gerald Rowan, listening intently, but did not enter a plea.
Crown prosecutor David Johnstone acknowledged the case was of high public interest.
However, he sought "somewhat extensive suppression orders" including the accused, the second injured officer and the member of the public injured in the incident.
The reason for the suppression was to "protect the integrity of the investigation" - dubbed Operation Wheaton.
"Police have a significant amount of work to do on this inquiry," Johnstone told the court.
There was a fear that evidence given witnesses to the alleged murder, attempted murder and dangerous driving may be affected if they were to see the man in the media.
Media applications to film and photograph the accused were refused for now, but would be addressed more fully when the matter was next called in the High Court at Auckland.
Johnstone did not seek suppression for Hunt, who had earlier been named by police in an extensive statement.
Defence lawyer Mark Edgar said the case had received an "inordinate amount of media coverage" in the past 24 hours.
He said it was vital to preserve his client's fair trial rights in that respect.
He sought an order suppressing all details about his client and objected entirely to the man being filmed or photographed.
The accused was remanded in custody and will next appear in the High Court on July 8.
