"We are working hard to gather as much information as we can to piece together all the circumstances surrounding her tragic death," Mr Schmid said.
"We are making progress, and we are grateful to those members of the public who have contacted police as a result of our appeals for information and have assisted our investigation.
"These are very serious injuries inflicted upon an innocent baby less than 4 weeks old. The very nature of those injuries are deeply concerning. I continue to urge anyone who has yet to contact police to come forward; we know there are people out there who hold vital information about this case."
Anyone with any information was asked to contact the Kaitaia police on (09) 408-6500, or Crimestoppers, anonymously, on 0800 555-111.