Tom Phillips. Photo: Supplied
Phillips died in a shootout with police in the early hours of Monday last week, after spending nearly four years on the run with his children.
"There's a number of questions I think that need answered, and so it is my expectation there would be an inquiry as to how government agencies have acted over the last four-year period," Luxon said.
He said there are "legitimate" questions to ask of how police and Oranga Tamariki handled the case.
"An inquiry into how government agencies have acted, essentially . Exactly what form that needs to be, we'll take advice."
Cordons on Te Anga Road in the Waitomo region were removed at the weekend, nearly a week after Phillips' fatal interaction with police.
