The workers, Tshering and Sonam, who only wanted to be referred to by their first names, are both from Bhutan and supporting their husbands and children.

They are desperate to be reinstated to their jobs which are their only means of survival in Australia.

They fell asleep in the day surgery waiting area - while all theatres were closed - about 4am during their designated unpaid break, behaviour contractor ISS labelled a "serious breach" of the company's code of conduct.

ISS did not respond to multiple requests for comment from The Canberra Times on Tuesday.

Tshering has worked as a cleaner at the hospital for one-and-a-half years while Sonam has worked there for three years.

The permanent workers were employed by ISS, which Canberra Health Services contracts cleaning services to.

After being contacted by The Canberra Times, ISS reportedly told the workers it was reviewing their terminations.

The women said they accidentally fell asleep on their unpaid breaks after working five or six hours without taking their paid break.

The workers admitted to having received a warning about a year ago for sleeping at work, however this time they were undisputedly on their break.

While union United Voice has maintained the women did nothing wrong by sleeping on their break, the workers wrote contrite letters of apology to ISS begging to keep their jobs.

"Up until now there hasn’t been any flaws recorded against my work-related competency/performance," Sonam said in the letter.

"It's very unfortunate that very recently I have fallen asleep on duty which I sincerely admit and regret for slipping into sleep while on duty.

"Should I ever repeat in future I would not expect any apology rather on spot termination may be delivered."

Tshering said: "Please accept my deepest apologies for the misconduct I was involved at work.

"I am sorry is the very small word to say against my shameful misconduct but the burden of shame is utmost and it's bending my stature to knee-level."

But on Tuesday the women were told they would be sacked.

United Voice ACT secretary Lyndal Ryan said she wanted ISS to be big enough to realise it had made a mistake in sacking the women.

She wants ACT Health to intervene and call on ISS to reinstate them.

"This is big multinational company and they can afford to treat people badly," Ms Ryan said.

She said it was part of a wider problem that started with ACT Health contracting out jobs, resulting in workers losing their rights.

ACTU president Michele O'Neil said she was shocked by the dismissals.

"It's an unpaid break you should have a right in Australia to do what you need to do in an unpaid break," she said.

"It's callous and unreasonable and unfair for them to be sacked."

Canberra Health Services said it would be inappropriate to comment because the matter was that of the contractor’s.