The first four boys were rescued Sunday night after 16 days in a cave in Thailand, and the eight other youths and their soccer coach will attempt the journey hours later. They will be shuttled to helicopters that will take them to a hospital.
Each rescue operation takes around 10 hours.
Billionaire tech developer Elon Musk had also offered to provide assistance, in the form of a "kid-size submarine", which could arrive in Thailand early Monday, local time.
His news of creating an escape pod came after USA and Thai officials got four boys out of the flooded cave network after spending 15 days trapped along with their soccer coach.
"The operation went much better than expected", said Chiang Rai acting governor Narongsak Osatanakorn, who is overseeing the mission.
Media members walking to the area opposite the hospital said that reporters, hospital staff members or nearby residents were not allowed to take photos by camera or phones in the area or officials guarding the front area would confiscate their devices.
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Extracting everyone could take four days, but Sunday's success raises hopes
Meanwhile, the rescue team at the Tham Luang cave complex decided that the situation was too dire to wait any longer. One of the boys, identified as Tun, wrote: "Mom and Dad, please don't worry, I am fine".
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There was no official announcement as to which four boys the divers were able to bring through the cave.
The Thai Navy said Saturday three navy SEALs, one a doctor, were with the boys and coach.
Thirteen foreign divers and five members of Thailand's elite navy SEAL unit are trying to bring the boys - some as young as 11 and weak swimmers - through narrow, submerged passageways that claimed the life of a former Thai navy diver on Friday.
REUTERS/GETTYThailand cave rescue update: Have all the boys now been rescued?
Thailand's Meteorological Department said there was a 60 per cent chance of rain with more thunderstorms forecast throughout the week.
An official reportedly told a Thai TV station on Monday morning that they didn't want to name the boys because "they're afraid it will affect the parents of kids who still remain inside".
Information slowly started to come out about the boys' nine-day ordeal before they were eventually found on Monday night, through letters and limited communication between the coach, the team and the rescuers who have been with them in a small cave chamber.
An underwater rescue pod fashioned from a SpaceX Falcon 9 liquid-oxygen transfer tube undergoes testing in a California swimming pool. I'm happy being here inside, the navy SEALS have taken good care.