Two people on board a sinking yacht have survived “quite extreme” conditions to be rescued from the stricken vessel after a multi-agency operation that ran through the night.

The Australian Maritime Safety Authority confirmed a 60-year-old man and a 48-year-old woman who were on board the 19-metre yacht were rescued about 7.25am on Tuesday.

The pair are believed to be uninjured, but the boat – the Spirit of Mateship – had to be abandoned.

AMSA said it received a distress beacon alert about midday on Monday, but choppy conditions due to strong winds plagued rescue efforts.

A mechanical failure led to the yacht becoming stranded around 185 kilometres east of Nowra. It drifted further east to sit about 300 kilometres offshore before the duo were saved.

Navy vessel HMAS Canberra assisted in the rescue, as did NSW Police vessel Nemesis.

HMAS Canberra’s captain Brendan O’Hara said the duo’s near-24-hour ordeal would have been torturous, given his far-more-sizeable ship had also battled the powerful swells.

Winds of between 50km/h and 70km/h along with seas of up to six metres had made executing the rescue effort challenging for crews, conditions O’Hara labelled “quite extreme”.

“[The pair] were just holding on as best they could … I hate to think what it was like for them, because even on board Canberra, which is quite a large ship, we were rocking and rolling a fair bit,” he told Seven’s Sunrise program.

“Not much of the crew here have had much sleep, so the two personnel in Spirit of Mateship definitely had no sleep at all, I dread to think about the conditions in there.”

AMSA duty manager Ben Flight said the rescued pair were believed to be in good shape considering the ordeal.

“We’ve safely recovered the two people on board the police vessel Nemesis … we understand, all things considered, they’re in good conditions,” he told Sydney radio 2GB.

“The police vessel Nemesis and the HMAS Canberra are both heading back towards the coast and we understand they’re going to go back to Sydney tonight to take the two people off.”

HMAS Canberra arrived on scene at 1am on Tuesday, while the police boat got there at 3am.

The duo will be taken back to Sydney for medical assessment.

The choppy conditions initially prevented authorities from winching the duo out of their boat and airlifting them to medical facilities.

Earlier on Tuesday, AMSA officials said the matter had become “time-sensitive” with the boat taking on water.

Two Royal Australian Navy ships and an RAAF C-130J Hercules aircraft were initially involved in the rescue operation.

The Spirit of Mateship has previously been a Sydney-Hobart yacht, crewed by wounded and injured former defence force personnel to raise money for charity Mates4Mates.

Rescue in Tasmania

Further south, Tasmania Police said they were “gobsmacked” that a group of more than a dozen bushwalkers, including three children, had to be rescued from treacherous conditions on the summit of kunanyi/Mount Wellington.

Temperatures on the snowy Hobart mountain have been below -3 degrees while wind gusts reached up to 109km/h as this week’s wild weather has passed through.

The weather bureau said there was a feels-like temperature of -21.6 degrees amid heavy snow on Monday night.

Police said a stranded group of 13 people called for help as the weather closed in on Monday afternoon.

They had mobile phones but “minimal food and water, and no equipment to spend the night in case of emergency”.

Hobart Mayor Anna Reynolds said they sheltered in the observation deck at the mountain’s summit, at an elevation of 1271 metres.

Police liaised with City of Hobart authorities for the rescue. In a surprise development, council workers on their way up in the mountain in four-wheel drives behind a tractor with a snowplough stumbled on another group of five walkers on their way down.

Reynolds said that group had to be rescued first.

“It was very lucky for them that our staff were going past and they were on the road,” she told the ABC.

She said three of them “were in a very bad way”.

Earlier, City of Hobart chief executive Michael Stretton said “we can’t guarantee that we’ll always be able to rescue stranded walkers so visiting the mountain in these extreme weather conditions comes with high risk”.

Police Inspector Darren Latham said it was frustrating that police had to constantly warn walkers on Mount Wellington – especially during bad weather.

“The Bureau of Meteorology, the SES and Tasmania Police have been issuing warnings to the community regarding the severe weather event since last week. This included several bushwalker weather alerts,” he said.

-with AAP