Middlemiss said a large number of officers are involved in the investigation.
“We have executed a number of search warrants in relation to the incident, however, Murray and the weapon involved remain at large.”
Police were already looking for Murray before the Titahi Bay shooting.
Wellington police posted a picture of him on their Facebook page on March 16 - the day before the shooting incident - saying there was a warrant for his arrest.
Police told NZME they could not release further information “about this incident and this person at this time”.
Middlemiss said Murray is not thought to be a direct threat to the public but he could be armed and should not be approached.
He is actively avoiding police and could have travelled to Hawke’s Bay, where he has ties.
Anyone with knowledge of his location should ring 111, police said.