Rescuers now have to decide how best to get the group out in their weakened condition.
Their rescue brought hope in a desperate search that attracted global help and captivated the Southeast Asian country.
Mr Narongsak said the passageway the divers were making their way through goes upwards in some places and downwards in others and is extremely narrow, making it hard for divers to fit through with all their gear.
"We categorised their health condition as red, yellow or green, red being the most severe injuries, yellow being mild and green being light". Experts have said it could be safer to simply supply them where they are for now. That could take as long as months, however, given that Thailand's rainy season typically lasts through October.
After 10 grueling days of uncertainty about whether or not the Thailand soccer team members and their coach were alive, one member of the worldwide rescue team breathed a huge sigh of relief today.
At Mae Sai Prasitsart school, where six of the missing boys studied, special prayers were held for the junior soccer team during the morning assembly on Monday.
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A pair of expert cave divers from Britain found the group about 300-400 metres past a section of the cave on higher ground that was thought to be where they might have taken shelter.
"You are very strong", one of the rescuers says in English. "Brilliant", one of the British rescuers responded as the boys confirmed that all 13 team members were present and accounted for, reports CBS News correspondent Ben Tracy.
One of the boys is heard to say: "Eat, eat, eat, tell them we are hungry".
"If you ask me now while we are still assessing all sides then I don't think they will be home soon", Chiang Rai governor Narongsak Osottanakorn told reporters.
Pipob Udomittipong, foreign affairs commentator, said he was unsurprised the small foreign team discovered the group first instead of Thai rescuers - comprised of hundreds of officers.
"It is not a hundred percent secure", the governor said Tuesday.
He said: "We found that most of the boys are in green condition".
Everything depends on how hard the dives are.
He described taking non-divers through a cave as "one of the most risky situations possible, even if the dives are relatively easy". For now though, Captain Akanand Surawan, a commander with the Royal Thai Navy, said authorities would now supply the group with four months' worth of food and also begin teaching the boys how to scuba dive.
The worldwide rescue operation - which includes the Thai Navy SEALs as well as experts from the US, China, Australia and the United Kingdom - had been working to reach a large, deep chamber, informally named Pattaya Beach, where they believed the missing boys had taken refuge. "They really did the final prep work to find them".