Nauru rape victim to get abortion in Aust

A female asylum seeker raped on Nauru has been transferred to Australia for an abortion.

The 23-year-old Somali woman last week made a public appeal to Prime Minister Malcolm Turnbull to allow her to travel to the mainland for a termination.

"You've got to wonder why a young woman's very distressing situation had to become so public and the minister had to be pleaded with by the Australian people," Greens senator Sarah Hanson-Young told reporters in Canberra on Monday.

Meanwhile, Nauru police have closed their investigation into claims a 26-year-old Somali asylum seeker was raped.

The Nauru government, in a statement, said there was "insufficient evidence" to support the woman's claim she was set upon by two men and dragged inside a cave and raped for about 30 minutes.

The woman was unable to identify her alleged attackers, saying they had covered their faces with t-shirts.

"The only information she was able to provide police was that that they were of muscular build and talked in Nauruan," the statement said.

There was no evidence of the victim's clothes being ripped or shredded and no visible cuts to the body indicating an attack.

Hospital tests proved negative for rape.

Police had also been unable to find the cave.

The Nauru police said the case would be reopened if new evidence came to light.