Two gay refugees who fell in love at the Nauru detention camp say they are virtually prisoners in their home: holed up in fear for their lives after being bashed and verbally abused in a nation where homosexuality is illegal.

As Sydney prepares for Saturday night's Mardi Gras parade - an event that showcases Australia as a global model of acceptance of gay and lesbian people - the federal government is refusing to rescue the two young Iranian men it sent to a country where they could be jailed for their sexual orientation, according to lawyers.

A digitally altered photo of two gay Iranian refugees, Nima and Ashkan, who say they are being persecuted at Nauru, where homosexuality is illegal.

Immigration Minister Peter Dutton has so far refused to help the refugees, who say they have been repeatedly beaten, had rocks thrown at them and been called "human rubbish". His department says refugees at Nauru can accept resettlement in Cambodia.

The Human Rights Law Centre and international LGBT rights group All Out have begun a petition calling on Prime Minister Malcolm Turnbull to urgently intervene and bring the men to Australia. The refugees, known by the pseudonyms Nima and Ashkan, live in the Nauruan community. They say they spend their lives confined in a tiny unit with the doors locked and window shades drawn - leaving just once a week to buy food, escorted by a case manager.