The Maersk employees were onboard the Nan Hai 6 drilling rig when the fire broke out in a storeroom on Sunday afternoon, according to News Ltd and ABC Radio news reports.

The rig, which can house 92 workers, had recently been stationed at the Kuda Tasi-3 exploration well in the Timor Sea, 575km northwest of Darwin.

The employees are now being treated at Royal Darwin Hospital.

One worker suffered burns to the hands and face and is in a serious but stable condition. The other is in a stable condition with burns to the hands.

Maersk and Woodside have sent a joint investigation team to investigate the cause of the fire.

But the Maritime Union of Australia told ABC Radio that it had been worried about safety on the rig for several months.

"On this particular rig they reckon it's one of the worst ones they've actually worked on compared to some of the other rigs that have come down to Australia," the union's Mick Killick told the news broadcaster.

"There was a range of mechanical and electrical safety issues on board, we tried ever since the rig came to Australia to get access for an inspection, have a meeting with a company all to no avail, it all just fell on deaf ears."