Alleged sex crimes against asylum seekers, worker misconduct and cases of typhoid and tuberculosis were not reported to the nation's workplace safety watchdog, showing the federal government is aiding a "cover-up" of alarming conditions at the Nauru detention camp, a lawyers group says.

Data released under freedom of information laws to the Australian Lawyers Alliance shows serious incidents uncovered by the damning Moss review, and others detailed to a Senate inquiry, were not reported to Comcare, the nation's work safety regulator.

The Australian-funded asylum seeker processing centre on Nauru.

By law, the Department of Immigration and Border Protection must report a death, serious injury, illness or dangerous incident arising from the conduct of a detention centre's operations.

However, the department rejects claims of wrongdoing and says incidents cited by the alliance did not necessarily need to be reported.