Narongsak Osotthanakorn said the boy's rescue involved numerous same divers who brought the four boys out Sunday.
And while the health experts are being cautious, all accounts suggest the boys are in good health - and even better spirits.
Narongsak said after the first four boys were rescued that they would be quarantined "for a while because we are concerned about infections".
The boys, ages 11-16, and their 25-year-old became stranded when they went exploring in the cave after a practice game.
The boys are all part of a Thai soccer team that went missing weeks ago - before they were found on a rock shelf deep in the flooded cave.
It could take two to four days complete the mission, officials said.
The effort to save the boys and their coach has involved both foreign divers and members of an elite Thai navy unit.
Authorities have been tightlipped about the progress of Monday's operation. Narongsak on Monday said their identities were being protected out of respect for the families of those still trapped inside the cave.
How long will the rescue operation take?
The four who were rescued previously were taken to a hospital in Chiang Rai for evaluation.
The operation resumed after a 10-hour hiatus. It was unclear who was inside the ambulance or the helicopter.
It is unclear which boys have been pulled out and which still remain in the cave.
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One boy was rescued Monday, the Thai navy confirmed.
Authorities had said that incoming monsoon rains that could send water levels in the cave rising, coupled with falling oxygen levels in the enclosed space, added to the urgency of getting those trapped out.
Interior Minister Anupong Paochinda told reporters the rescued boys were in good health in hospital but did not give further details.
Emergency crews in Thailand have reportedly brought another member of a soccer team to safety, weeks after 12 boys and their coach were trapped in a flooded cave network. Musk said his submarine has eight handles, four in the front and four in the rear, and four air tank connections.
There was no word on the condition of any of the people brought out on Monday. It takes the divers about eight hours to get into the cave, reach the boys, and bring them back out. Weather forecasters said heavy rain could hit the area on Monday afternoon and continue through the week. All four boys are being treated at a hospital in Chiang Rai, the nearest major city.
The first four rescued boys have been placed in a ward set aside specifically for the cave rescue, a source at the hospital said. Billionaire tech entrepreneur Elon Musk was the latest to pitch in.
The film and television studio also posted a video of Scott on their official Twitter handle. "Testing for 3 more hours in LA, then it's on a plane to Thailand", Musk tweeted.
Among those are USA military partners, British cave diving experts - including the two men who first located the boys a week ago - and rescue workers from Australia, China and other countries.
The first kilometer is the hardest, CNN explains, as that's where the children have to navigate a narrow flooded channel.
A Reuters witness near the Tham Luang cave in the northern province of Chiang Rai saw medical personnel carrying four people out of the cave to waiting ambulances over the course of the day.
Progress came more easily on Monday, with replenished oxygen tanks and tightened guide ropes.