A 23-year-old "vulnerable and traumatised" Somali woman who was raped on Nauru is pleading with Prime Minister Malcolm Turnbull to allow her to come to Australia to have an abortion.

The woman, "Abyan" (not her real name) is one of two female Somali refugees who have requested help from Australia after being raped on the island. Last week the ABC's 7.30 broadcast distressing footage of the other victim, a 26-year-old woman known as "Namja" (not her real name), calling police for help after her rape - she says it took police four hours to answer her plea.

The 23-year-old woman is 11 or more weeks pregnant as a result of her rape and is begging to be allowed to come to Australia for an abortion. It is illegal to have an abortion on Nauru.