The advocacy and support group, the Refugee Action Coalition, says the two men - aged in their 20s - were in the Lorengau refugee settlement area on Manus Island when they were arrested and beaten by Papua New Guinean police and immigration officials.
It released photos it says show the Iranians' partially swollen faces marked by cuts and bruises, and injuries to their bodies.
Spokesman Ian Rintoul says they were on their way to New Year's Eve celebrations when they were allegedly assaulted.
"They were first approached by immigration police who told them they have no right to be outside of the detention centre. They were quickly then joined by PNG police. Subsequently they were quite savagely beaten and then taken into police custody. There are no particular charges, but there are quite serious injuries inflicted on these two people for absolutely no reason."
Mr Rintoul says the men were held in police custody for over 35 hours, during which time they were denied medical care.
He says International Health and Medical Services, the agency providing medical care to detainees inside the Australian processing centre, was on standby to see them after their release.
"It looks like one of them has got a broken nose, the other possibly a broken wrist. The wrist is swollen and malformed. One thinks he may have a broken jaw. He has not been able to move his jaw. He has not been able to drink or eat while he has been in custody."
But Manus Island MP Ronnie Knight says the two men were engaging in anti-social behaviour, and were under the influence of drugs and alcohol when police found them.
"They were making a nuisance of themselves, stopping traffic, harassing people on the road, chasing young girls, making idiots of themselves."
Mr Knight alleges they also caused a fight with police officers.
He has defended the actions of PNG police.
"What happened to these two young fellows is not anything that doesn't happen to our people when they get out of line. They get the same treatment. And to defend my policemen, here in Manus we are outnumbered, we are undermanned, and in situations like this, there is no option but they have to be brutal to put an end to what they're doing really quick. And that is the fact of life in Papua New Guinea at the moment. This is not Australia. if you're in Papua New Guinea you abide by PNG law."
The Australian Immigration Department says it cannot comment on the incident because it is a matter for PNG police.
Immigration Minister Peter Dutton, meanwhile, suggested to radio 2GB that refugee advocates are trying to use the cases to attack the government's immigration policy.
He said what actually happened is not yet clear.
"If people have had an interaction with the PNG police on New Year's Eve night, I would wait to see the full facts of that case before I make any comment to say that they were targeted because they were refugees or because they were part of the Manus Island population."
Ian Rintoul from the Refugee Action Coalition says the Australian government is responsible for detainees on Manus Island, and should investigate.
He says the two Iranian men's experience highlights issues compromising the safety and security of asylum seekers and refugees on the island.
"Perhaps more immediately the government could do something about ensuring that there are proper lawful processes. That there are inquiries. That people get the medical attention that they need."
