The eggs were found to be missing on Thursday morning during routine checks.
DOC Compliance officers and police are investigating, with support from the Royal Albatross Centre and mana whenua.
DOC Coastal Otago Operations Manager Annie Wallace says this is a very unusual event.
"The colony has been managed and monitored for years, and it's strange for eggs to disappear without a trace."
"It's still unclear what has happened, and we are gathering security camera footage and talking to people who may have relevant information. However, it's thought the eggs may have been taken as there are no signs they were eaten by predators."
Annie Wallace says toroa are nationally vulnerable and threatened by climate change, fishing practices, plastic pollution, and habitat loss. They also reproduce slowly, so all eggs and chicks are important to the population.
"They need all the help they can get, and it will be extremely disappointing if someone has taken these eggs.
"This is devastating for our staff who put in countless hours caring for these birds in challenging conditions, keeping them cool on hot days, working to prevent flystrike, and providing supplementary feeds to underweight chicks."
Te Poari a Pukekura Management Group Chair Nadia Wesley-Smith says, "the disappearance of toroa eggs from Pukekura is deeply concerning, and considered by Te Poari a Pukekura as not only a disruption to the mauri and mana of the headland, but also has a devastating impact to the toroa population, and the conservation efforts of all who care for our taoka species".
Te Rūnanga o Ōtakou Chair Rachel Wesley said the hapū from Ōtākou have a close affinity with the toroa at Pukekura, so we view the unexplained disappearance with the utmost concern.
"Due to the slow breeding cycle and vulnerable status of toroa, any loss of eggs or chicks from natural causes is disappointing, but the unexplained nature of this particular incident, and especially with the suggestion it may be people who are responsible, is absolutely devastating.
"I hope answers to their whereabouts will be found quickly and the eggs of this important taoka species still remain viable."
Taiaroa Head is the only mainland site in the world where toroa breed, and one of the few places in the world where people can easily see them. It's a privilege that people need to respect, Annie Wallace says.
The site is a nature reserve and is fully fenced, and entry is by permit only. There is also a Wildlife Foreshore Sanctuary along the coast which restricts both foot and boat access.
If anyone has any information that might help find these eggs, they are asked to call 0800 DOC HOT (0800 362 468) or the Police non-emergency number 105.
Toroa are one of the largest seabirds in the world, with a wingspan of more than 3m. There are about 17,000 of these long-lived birds left, and they range widely across the Southern Ocean. Most breed on several islands in the Chatham Islands.
Toroa are protected under the Wildlife Act and it is an offence to kill, injure, harass or disturb them.
