The two people injured in a fatal shooting in Hamilton early on Sunday morning remain in hospital in a serious and critical condition.

Robert Nelson, 23, was shot dead at the Melville address.

His 20-year-old girlfriend is in Waikato Hospital in a serious but stable condition, while a 17-year-old male remains in a critical condition in the Intensive Care Unit.

Police say the house in Matthews Crescent, where the incident took place was targeted.

They say a number of shots were fired at the house at about 1am and those in the house were getting ready for bed at the time.

Police are still looking for the person responsible for the shooting.