Officers said they were 'very concerned' at the level of violence used. Detective Chief Inspector George Brown, of Lothian and Borders Police, said: 'This was a particularly brutal attack. It is vital that we track these people down. We must expect them to strike again.'
It was too early to say whether the rape of another man in the city in July was linked to the latest assault. 'There are similarities. We are not ruling anything out,' Det Ch Insp Brown said.
The man, who suffered massive internal bleeding during the assault in August, is waiting for the results of tests to determine whether he has contracted HIV, the Aids virus.
In an interview with the Independent, the victim described the attack.
'I met a man in a gay bar in the New Town,' he said. 'He seemed nice. He asked whether I lived alone. We went back to my flat and he suggested that we go to the bedroom. We had just started to undress when a second man appeared. The first man must have opened the front door when he went to the toilet.
'I said, 'what's going on?' They started kicking and punching me all over. Then they held me down and took turns to rape me.
'They were laughing, saying that this was what I wanted. You name it, they did it to me. It went on for hours and I lost consciousness.
'When I came to, I saw there was blood all over the room. I was coughing up blood for weeks afterwards. I stayed alone in my flat for four weeks hardly eating. I did not see a doctor and I became very weak. I couldn't face anyone.
'A few weeks after the attack, one of the men telephoned me and said he had photographs of me being raped, which he would distribute to my neighbours and put up in gay bars if I did not hand over money. These people are not human. They could kill someone.'
The Glasgow City and National Liaison Group, the self-help organisation which has been counselling the victim, said there have been five male rapes in Edinburgh in the last two months.
Brian McKenna, the group's chairman, warned that the photographs and the demands for money could be 'a sinister development' in a homosexual blackmail scandal that emerged in Glasgow earlier this year.
Last month Paul Mellon, 26, was jailed for four years after Glasgow High Court was told that he had extorted pounds 17,000 from a 62- year-old businessman who had been his lover. Mellon had threatened to expose the businessman's homosexuality.
Eight more extortion cases come to court in Glasgow next week. More than 40 other men are discussing legal action with the Liaison Group.
The attackers are described as about 35 years old. One is about 5ft 9in tall, slim with brown hair and a beard. The other is of medium build, with collar-length, dark hair.