A Somali refugee who became pregnant after allegedly being raped on Nauru has arrived in Australia for an abortion.

The woman, 23, had appealed for weeks to be transferred from the island, part of Australia's offshore network housing people seeking asylum.

Australia's top court is currently reviewing the legality of the centres.

Thousands of Australians rallied over the weekend in support of refugees and demanding their closure.

Meanwhile Nauru has dismissed another Somali refugee's allegation she was raped.

The authorities said there was insufficient evidence to support the woman's claim she was raped by two Nauruan men.

Under Australia's tough asylum policy, any irregular migrants trying to reach the country by boat are intercepted and held in centres on Nauru and Manus Island, Papua New Guinea.

The government says this deters people-traffickers but there have been criticism of the conditions at the camps.

Australia and asylum

Caption: The weekend saw demonstrations supporting refugees

• Many asylum seekers - mainly from Afghanistan, Sri Lanka, Iraq and Iran - travelled to Australia's Christmas Island by boat from Indonesia.
• The number of boats rose sharply in 2012 and early 2013. Scores of people died making the journey.
• To stop the influx, the government adopted hard-line measures intended as a deterrent.
• Everyone who arrives by boat is now detained and processed in Nauru and Papua New Guinea. Those found to be refugees will be resettled in PNG, Nauru or Cambodia.

The 23-year-old Somali woman is reportedly more than 12 weeks pregnant. Abortion is allowed in some circumstances on Nauru but not in the case of rape.

The Australian government had come under pressure to allow her to enter the country to terminate the pregnancy.

"Our client is relieved that there has been a resolution to this sensitive matter," her lawyer George Newhouse told the Sydney Morning Herald.

"She is now in Australia and the Commonwealth government has agreed to provide her with medical treatment."

But an opposition politician hit out at the woman's treatment.

"You've got to wonder why a young woman's very distressing situation had to become so public and the [prime] minister had to be pleaded with by the Australian people," said Greens senator Sarah Hanson-Young, AAP reported.