An asylum seeker woman in Nauru has alleged she was raped twice by a male asylum seeker, whom she claims was immediately given a visa by the Immigration Department after she complained about the assault.

In a letter obtained by Fairfax Media, the single mother says that she was initially "troubled by a married man" in the family compound of the offshore processing centre on the small Pacific island.

A file picture of asylum seekers on Nauru. Credit:Angela Wylie

Writing through an English interpreter she says: "I explained my situation to [psychologists] and asking [sic] them to transfer me to singles camp but they did not take it serious till that man raped me." She says there were two witnesses to the attack.

The woman, whose name has been withdrawn by Fairfax Media, claims that after she reported the sexual assault to the psychiatrist on the island, the Immigration Department "immediately" gave the alleged offender a positive refugee status determination, offering him a temporary Nauruan visa.