Police were called at 1.20pm, and despite a search by two inflatable boats, Taranaki Coastguard, about 40 police personnel and a plane, there has been no sign of the instructor or the two boys.
The other nine members of the climbing party were taken by helicopter to hospital, where they were treated and discharged with no sign of serious injuries.
Incident controller, Inspector Frank Grant spoke at a media conference tonight.
"Given the current situation, we have grave fears for their safety, but we remain optimistic,'' he said.
Police were not sure what equipment was being used by the climbers, and it was unclear which route up the rockface they had taken.
The search, stretching from four to five kilometres north-east of Paritutu Rock south-west towards Oakura _ has been called off for the night, and a briefing will be held at 7am tomorrow ahead of the rescue effort resuming.
The police dive squad and the Air Force will join the search.
Police say the names of the missing three may be released tomorrow, once next of kin have been advised.
Where the search is ongoing:
View New Plymouth missing climbers in a larger map