Police were not aware of any issues between the two men, but anyone who had any information that might aid the investigation was urged to contact the Kaitaia police station on (09) 408-6500, or Crimestoppers, anonymously, on 0800 555-111.
"Clearly we believe some significant event has occurred, but it's still a missing person enquiry," DI Burke said.
Police had been to "countless" addresses looking for Mr Moore, an inquiry team working through Easter weekend and completing scene examinations at three properties in Kaitaia and Peria.
They had discovered some "items of significance," and while he declined to reveal what those items were he said they would help with the investigation.
Mr Moore's family were becoming increasingly concerned for his health, as he required medication.
Mr Moore is described as 1.82m tall with dark hair and of solid build, while Yates is described as 1.73m tall and obese.