The man accused of carrying out a series of violent attacks in the Auckland suburb of Epsom had his court appearance postponed because he is in hospital.

The 49-year-old allegedly assaulted a jogger, stole a car and drove it into a group of high school students on bikes, and killed a dog before police tasered him, eight minutes after the first 111 call was made.

He was due to appear at Auckland District Court on Thursday, but instead, his counsel, Jane-Frances O'Halloran, asked for more time to be able to talk to her client.

He was at Auckland Hospital due to medical concerns, but under close police supervision.

Judge Grant Fraser suppressed the man's name on an interim basis and allowed him to appear in court via an audio-visual link on Monday afternoon.

He would be remanded in custody after his medical concerns were dealt with.

He faced 14 charges including multiple accounts of wounding and injuring with intent and assault with a weapon, as well as ill treatment of an animal.