A spokesman for Mr Morrison would not confirm reports the children had been evacuated.
"Any health transfers occur in accordance with standing policies," he said.
"Health services are constantly reviewed to ensure they are provided to the appropriate standard."
Fairfax has reported the Nauru government expressed concerns about the children's risk of self harm, which led to the medical evacuations.
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Operation Sovereign Borders: The story so far
Greens immigration spokesman Sarah Hanson-Young says the claims highlight the cruelty of the government's asylum seeker policies.
"We've seen reports today that four unaccompanied minors have had to be removed from the island prison on Nauru after being sent there, under what is incredibly cruel and harsh circumstances.
"One of those children is a young teenage girl all on her own. She has been used as a human ping pong ball bounced from cruel detention centre to cruel detention centre.
"It is simple unacceptable. It is is shameful to see the life of a child being used for this political game by the government."
