They were rescued over several hours on Saturday in an operation involving three vessels scouring the waters off Vietnam's central coast, according to a sailor aboard one of the rescue ships.

Kalmaegi crashed into the country's storm-battered middle belt on Thursday, killing at least five people after leaving more than 200 dead in the Philippines.

Phan Hau, 40, whose boat pulled one of the three men to safety, told AFP: "We were completely stunned -- it felt miraculous."

"None of us thought (he) could still be alive. Most of the 10 of us on board believed we were only searching for his body, not that he'd still be breathing."

State media reported the three men went missing Thursday afternoon after one of them, 44-year-old Duong Quang Cuong, jumped into the water after a family dispute.

Le Quang Sanh and Pham Duy Quang rowed out with life jackets in a tiny boat to try to rescue Cuong, but the vessel overturned and all three were carried far from shore, eventually becoming separated.

Quang was first to be rescued on Saturday morning by the Hai Nam 39 vessel south of Ly Son Island, where the men initially departed, state media said.

The Hai Nam 39 then radioed the port authority for help, which dispatched the An Vinh Express, according to its sailor Hau.

It took two hours for the second rescue ship to reach the area where Quang had been floating in his life jacket, and the crew began a painstaking search of an ocean current running southward from there.

"At first, when we saw Sanh, we didn't realise it was him. We had imagined Sanh wearing a red life jacket because, during the search, we were all looking for red objects to head toward. But he was wearing a black shirt, so we didn't think it was him," Hau said.

- 'Overjoyed' -

In a video Hau took on his phone -- metadata from which shows it was taken south of the previous rescue site and about a dozen nautical miles from shore -- Sanh is drifting alone in the current, as crew members shout his name and throw a life preserver his way.

Hau explained that Sanh had taken off the vest to wave it at a previous passing vessel, but it had been blown away in the surf.

Sanh was conscious but severely disoriented after so long at sea, asking his rescuers why they had come looking for him when he was "just taking a swim", according to Hau.

Cuong, the man who had initially jumped into the water, was finally rescued by a third vessel slightly closer to Ly Son, state media said.

It said all three men were in hospital as of Monday, with no official word on their precise condition.

"Quang's health is gradually stabilising... everyone across Vietnam is overjoyed," his wife Tran Thi Lau, 45, told AFP, confirming many of the details reported by state media.

"The happiness was overwhelming. His condition still isn't fully stable, so we're not sure yet when he'll be discharged from the hospital."