The identity of the man accused of shooting a police officer in the Manukau suburb of Papatoetoe will remain a secret until at least tomorrow.

The 28-year-old made a brief appearance in the Manukau District Court this morning charged with the attempted murder of Constable Jeremy Snow.

Constable Snow and his partner Robert Cato were on a routine patrol when they were shot at from the darkness at 4.10am on December 22.

They had been investigating a car that looked like it was being tampered with.

Constable Snow was shot three times, once in each leg and once in the elbow and lost a large amount of blood when one of the bullets went through his femoral artery.

Police spokeswoman Ana-Marie Gates-Bowey said Mr Snow was discharged from hospital last Wednesday after undergoing surgery and was "making some great progress".

Ish Jayanandan - the lawyer of the man charged with Mr Snow's attempted murder - argued for continued name suppression so the man's mother, who is out of the country could be told of the charges her son faces.

Ms Jayanandan also opposed in court media coverage and said she had not received the police files on the case and the identity of the man could be important to his case.

Judge Charles Blackie said disclosure of police evidence was not due and there was no reason for the name suppression to continue.

He said he would be treating the man the same as all those who had appeared before him.

Judge Blackie said he was "not impressed" with Ms Jayanandan's arguments and the principles of open justice applied.

He said the matter had been before the courts since December 23, when the man had a bedside court appearance at Middlemore Hospital, and there had been plenty of time to notify his mother.

Ms Jayanandan said she would appeal the decision and was given a deadline of midday by Judge Blackie.

Outside court, Ms Jayanandan confirmed she would be lodging an appeal.

The man is due to reappear tomorrow.

Police were looking for 43-year-old Darren Court who they say witnessed the shooting. Court was facing two outstanding warrants for arrest when police caught up with him.

Ms Gates-Bowey said police were continuing their investigation into the shooting and it was not yet clear if Court would faces charges in relation to the incident.