A group of sailors from HMAS Success has been sent home and an inquiry launched after they allegedly organised a challenge to have sex with as many female crewmates as possible.

The Seven Network reported the sailors detailed their contest in a document called The Ledger, where dollar values were placed on each woman during an overseas deployment in May.

Larger amounts were offered if the sailors could sleep with a female officer or a lesbian and sailors challenged each other to have sex in various locations, including on top of a pool table, the report said.

The arrangement was discovered while HMAS Success was visiting Singapore.

The captain ordered the sailors to return to Australia immediately after they were formally interviewed.

Mr Rudd said on Monday that he had seen the media reports and a statement from the Navy chief, Vice Admiral Russ Crane.

"Can I say I'm sure the Chief of Navy has all those matters under active investigation and that appropriate action will be taken," Mr Rudd told reporters in Sydney.

"These alleged behaviours are disturbing, but it's important also to get to the facts of it all and we'll await the investigations by the chief of navy to establish all those facts."