Samoan health authorities have stopped all children's vaccinations in the island nation after the deaths of two toddlers.

A full inquiry into the circumstances of the deaths has also been launched at the request of Prime Minister Tuilaepa Lupesoliai Sailele Malielegaoi.

The situation comes after two children, both aged 1, died minutes after receiving an MMR (measles, mumps and rubella) vaccination at Safotu Hospital, in Savaii, on Friday.

The youngsters have been identified as Lannacallystah Samuelu, daughter of Marietta and Samuelu Tuisuesue, and Lameko Siu, son of Punipuao and Timua Siu.

News of the deaths began to spread over the weekend after family members posted photos of the dead children - one wrapped in the arms of his distraught mother - on Facebook.

The public was officially informed by authorities yesterday, when Samoa's Ministry of Health chief, Dr Leausa Toleafoa Take Naseri, announced that all MMR vaccines in the country were to be seized after the deaths.

The nurses who administered the vaccinations have also been stood down and were being supported, he told local media.

In a statement, Malielegaoi described the incidents as "devastating" and said he was not taking this lightly.

"There are already processes that will determine if negligence is a factor," he said.

"And if so, rest assured those processes will be implemented to the letter - to ensure that such a tragedy will not be repeated and those responsible will be made to answer."

Families of the youngsters told TV1 Samoa they had made formal complaints with local police and were calling for investigations into their children's deaths.

The mother of one child told the station she asked that her son not get the vaccination after learning about the death of the little girl, which had occurred about two hours earlier at the same hospital.

It is alleged the nurse insisted that the vaccination go ahead and was given without consent.

University of Auckland vaccinologist Dr Helen Petousis-Harris said one death, let alone two, was extremely rare, and there had never been a death associated with the MMR vaccine in New Zealand.

She said although investigations were still continuing into what went wrong, there were two reasons that could have been factors in the deaths.

"One is that there's been an error where the vaccine is prepared for the injection incorrectly and ultimately results in the wrong substance being injected.

"Or there's been some sort of contamination due to the vaccine having been reconstituted and left at a room temperature for a really long period of time."

Petousis-Harris acknowledged that there could now be fears from parents about the safety of vaccines and immunisations.

But she said it was important for people to understand that the vaccine programme was a very safe one in New Zealand.

"The last thing you want is for people to be fearful of something that we know is actually incredibly safe.

"But right now, we have to try and understand what happened and then work out what can be done to ensure it doesn't happen again.

"It's exceptionally rare at the global level and will be taken extremely seriously."