The federal government says it plans to ensure all asylum seeker children on Nauru are off the island by the year's end.
Five more asylum seeker children have been evacuated from Nauru, leaving 17 on the island.
The children and their parents, from two families, were brought to Australia for medical treatment over the weekend.
"It's time to evacuate kids off the island, as quickly as possible, so that they can recover and rebuild their lives," Asylum Seeker Resource Centre campaign director Jana Favero said on Monday.
"It's time to end this national disgrace of a policy once and for all, and to pass laws that would prevent children from being held in offshore detention ever again."
The Kids Off Nauru campaign, started by World Vision and supported by more than 400 organisations, posted a message on Twitter, marking the evacuation of the children.
The federal government has confirmed all asylum seeker children will leave Nauru by the end of this year but insists they will not be permanently resettled in Australia, even if found to be refugees.
A total of 46 infants have been born to asylum seekers on Nauru since 2012.
In recent years, about 244 minors have been taken to Australia from offshore detention centres.