Police say they're following positive leads in their investigation of a fatal shooting in Hamilton.

29-year-old Michael James Thompson was shot at close range in Melville on Friday night, and died later in Waikato Hospital.

Senior Sergeant Pete van de Wetering says forensic experts have been over the murder scene, but the person who fired the shot hasn't yet been found.

He says locals should be cautious, but there's no reason to believe the offender will strike again.