Narongsak said the healthiest have been taken out first, and the next phase of the operation would start in 10-20 hours.
Four boys have so far completed the hazardous escape, according to rescue officials, and are receiving medical treatment.
The boys, all members of a local soccer team called the Wild Boars, had been hiking in the caves when they became trapped by rain waters. "We have to be 100 percent confident that there is no risk to the boys before we evacuate", provincial governor Narongsak Osottanakorn said. This caused the rescue mission to be expedited.
There will be two divers per child during the rescue operation, and the 12 kids and their coach will come out one-by-one.
The rescue mission has concluded for the night. They had been missing for 10 days before they were discovered.
She said members of the 353rd U.S. Special Operations Group and U.S. military pararescue teams, survival specialists, divers and medical personnel are on the ground in support of the Thai-led global rescue effort.
The Thai defence ministry said a team from a Musk firm with drilling and exploration know-how should reach the cave on Sunday.
The journey out the caves is risky and has already resulted in a former Thai Navy diver dying in the caves earlier in the week. The ambulances drove to a nearby helipad and a helicopter was seen taking off.
The announcement of US government involvement was sudden and this tweet is looked at as Trump's first public comment on the rescue mission. Each of the boys will be accompanied by two divers. The boys were rescued wearing full face masks.
The rescue mission began on Sunday morning, almost a week since the 12 boys, aged 11-16, and their coach had been discovered on an embankment 2.5 miles (4 kilometers) inside the winding tunnels.
The entire mission may last three to four days, as the boys are expected to come out gradually, officials said.
The group was found alive in a small cave chamber on Monday after nine days, mounting an global rescue effort with experts weighing in from all over the world.
While the initial strategy was to extract the strongest boys first, that was revised and the weakest were taken out after Dr Harris assessed their strength and health, Thai media reported.
Narongsak said Saturday that experts told him new rain could shrink the unflooded space where the boys are sheltering to just 10 square meters (108 square feet).
On Friday, officials warned that oxygen levels in the cave dropped from 21% to 15%, complicating rescue efforts.
The cave system, in a limestone mountain range bordering Myanmar in northern Thailand, has proven to be a formidable challenge for the global rescue coalition drawing some of the world's best divers who have volunteered to help in the operation alongside Thai Navy SEALs.
In places the passage is so tight divers have to take the scuba tank off their backs and carry their gear through one piece at a time.
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