Immigration Minister Scott Morrison has allowed 31 babies who were born to asylum seeker parents to remain in Australia and not be sent to Nauru.

Mr Morrison said the decision was a "one-off" and had come following "representations made by Senator Ricky Muir".

"Along with those 31 babies, I am also allowing their immediate family members to have their protection claims assessed in Australia," Mr Morrison said.

 "This includes their mothers, fathers and siblings. That is, around 80 family members, all of whom are already in Australia having been transferred from Nauru, for the birth of their child."

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