The Somali refugee who says she was raped on Nauru has thanked Australians who rallied to her cause and helped convince the government to bring her to the mainland for an abortion.

News of her arrival in Australia came as Nauruan police rejected claims made by a second Somali refugee she was also raped on the island where, under Australian government policy, asylum seekers who come by boat are sent for processing and resettlement.

The 23-year old woman, known as Abyan, is now more than 12 weeks pregnant and had been pleading with the government behind the scenes for a week but had not had any response to her request to have a termination in Australia. Abortions are forbidden on Nauru.

Fairfax Media first highlighted her case last week, after her requests for help went unanswered by the federal government. More than 61,000 Australians have since signed a petition calling on the government to allow Abyan to come to Australia for the specialist medical treatment she required.