The Somali refugee who says she was raped on Nauru and asked for an urgent abortion in Australia has been returned to the island, with claims she rejected treatment when it was offered.

Sources have told Fairfax Media the woman was being returned to Nauru on a charter plane, via the Solomon Islands capital Honiara, on Friday afternoon.

Lawyers seeking an injunction to prevent her return were told the Australian court system had no jurisdiction because she had left the country.

The woman, known as Abyan, was flown to Brisbane last Sunday and then to the Villawood detention centre this week so she could have an abortion in Sydney.