He said that the decision to try to rescue the boys and their coach was made because conditions inside the cave were the best they could hope for and that water levels were low enough after days of good weather that it was possible to walk through long stretches of the passage.
"Hooyah", the Thai Navy SEALs, who have played a crucial role in the against-the-odds operation, said in a Facebook post as they announced that a total of eight members of the "Wild Boars" football team had been rescued on Sunday and Monday.
As of Monday morning, nine people remained trapped in the cave, including the team's coach.
Doctors are monitoring them for any illnesses they may have picked up in the cave, and supervising efforts to build up their strength after they spent more than two weeks with little food and no natural light.
Somboon Sompiangjai, 38, the father of one of the trapped boys, said parents had been told by rescuers that the "strongest children" would be brought out first. Authorities have said extracting the entire team from the cave could take up to four days, but Sunday's success raised hopes that it could be done faster.
The rescuers are racing against time, as more rain is forecast, and the extra water would significantly complicate matters.
Officials have said storms forecast for Chiang Rai province in Thailand's far north had factored into their decision to go ahead with a complicated and unsafe plan for the boys aged between 11 and 16 and their coach to dive out of the cave.
Kanet Pongsuwan, the principal of the nearby Mae Sai Prasitsart School - which six of the boys attend - said that the rescued students will be eased back into the classroom.
Four of the boys were rescued yesterday, but nine remain underground including their 25-year-old fooitball coach, Ekkapol Chantawong.
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Mr Narongsak said discussions regarding the lowest risk rescue attempts were ongoing, but acknowledged that time was against them. Rescuers have been pumping water out of the cave with the goal of letting the boys walk out, rather than having to scuba dive.
The rescue of the remaining boys and their football coach is being carried out by trained divers who are helping them through the flooded cave network.
On Sunday, officials waited until several hours after the rescued boys had been transported to hospitals to announce their rescue.
The same elite divers involved in Sunday's rescue would conduct the next one, given their knowledge of the cave conditions, Thailand's interior minister said in a statement.
"Imagine marathon runners. It's like when they reach the finish line exhausted", said the source. Thai Navy SEALs later announced two more had been freed in what Gov. Narongsak Osatanakorn called a "very smooth operation".
"We have not been told which child has been brought out".
The names of the rescued boys were not released. Still, they were undergoing medical checks in a hospital and were not yet allowed close contact with relatives due to fear of infections, who were able to see them through a glass partition.
The extreme danger of the rescue effort was underscored last week when a former Thai Navy SEAL, Samarn Poonan, died after he fell unconscious while placing oxygen tanks deep inside the cave.
Rescue workers at the cave complex, seen late Sunday.
Osotthanakorn said the boys were hungry and asking for a Thai dish of beef with basil and chilli.