He said police were not looking for anyone else in relation to the incident at this stage.
An investigation would look at who fired the fatal shot and how many shots were fired, he said.
"What I do know is he was still alive (after the shooting) and police have spent some 25 minutes attempting to resuscitate him at the scene," Mr Boreham said.
Police did a "very good job in a very trying set of circumstances'' to keep the public safe during the incident.
"But when anyone is killed it's always tragic," Mr Boreham said.
Mr Boreham believed at least one person was hurt in the earlier home invasion but their injuries were not believed to be life-threatening.
Shots were fired at police in Waikato, on the Southern Motorway and in the Victoria Park tunnel in central Auckland, Inspector Kerry Watson said.
"We set up a myriad of tyre deflation scenes to try to slow the progress of that vehicle," Mr Watson told Radio New Zealand.
"As it was coming into Hamilton out AOS team from Hamilton got in behind it."
The vehicle was finally stopped on the Northern Motorway at Mairangi Bay, Mr Watson said.
The injured man was taken to hospital but died.
Police screened off the scene on the Northern Motorway near Sunset Road on the North Shore and asked motorists heading south into the city to not slow down while passing the scene.
The Auckland motorway was open, with the exception of the northern motorway between Tristram Ave and Constellation Drive in heading north.
Motorists were advised to expect delays.
The New Zealand Transport Agency said that traffic heading into the city was heavy and early morning southbound queues were several kilometres long as far as Oteha Valley.
"Even with the southbound lanes open, it will take some time to clear congestion - particularly with the heavy volume of traffic during the morning peak," NZTA's regional traffic manager Kathryn Musgrave said.
"We ask people to be patient and delays their journeys if possible - we will work as quickly as possible to clear congestion."
The NZTA said it has not been advised by the police when the motorway's northbound lanes would reopen and drivers heading north are asked to use the Northwestern (SH16) and Hobsonville/Upper Harbour (SH18) motorways.