Rescuers found them 10 days later and are now working to find a way to get them out.
The boys and their coach were exploring the cave when a sudden flash flood trapped them.
Thai officials are stressing that they may have to act very soon - meaning within the next couple of days. But if heavy rains start again, divers will try to take the boys out right away.
"The kids are healthy, coherent, having fun, playing with each other - they have some minor cuts and minor injuries only", said Chiang Rai Gov. Narongsak Osatanakorn on Saturday.
There was great concern over the dwindling air supply as the level of oxygen in the cave where the boys are trapped dropped to 15 per cent.
"We originally thought the boys can stay safe inside the cave for quite some time but circumstances have changed". It is only a small battle we've won, but the war has not ended.
He tweeted: "SpaceX team reached out to us today to help connect to Thai govt".
Another, identified as Tun, wrote: "Mum and Dad, please don't worry, I am fine. Tell Yord, prepare to bring me fried chicken to eat".
One boy named Mick wrote: "Don't be anxious, I miss everyone".
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Another boy, 13-year-old Sompong "Pong" Jaiwong, put on a fearless face: "Dear Mum and Dad, I love you".
However, the dive is complex - with one Navy SEAL dying during the rescue efforts - and numerous boys do not know how to swim. "I love everyone!" wrote Pheerapat, nicknamed "Night", who turned 16 underground.
The children urged relatives "not to worry" and asked for their favorite foods once they are safely evacuated. "Night loves you all", wrote Night, in the Thai manner of referring to oneself in the third person.
"Teachers, don't give us lots of homework!" read another.
The football coach trapped in a cave with 12 Thai boys has apologised to their parents in a letter sent out through divers. There are people taking really good care of them. "Thank you for all the support and please accept my apology".
Thai Navy SEALS released a statement on Facebook on Friday praising their former colleague. The 13 are having health evaluations and rehabilitation, and being taught diving skills. Dozens of locals are serving up food, water and medicine to rescue teams and the scores of media members who have descended on the remote forest park.
Thailand is holding its breath for the safe return of the group, with heavy rains forecast and fears mounting over the reduced oxygen and high level of water in the cave.
"Some are as deep as 400 metres. but they still can not find their location yet", Narongsak Osottanakorn told reporters, adding the mission lacked the technology "to pinpoint where they are staying".
The Thai Navy SEALs, who are leading the risky operation to get the boys out, posted images of the letters on Facebook.
The letter that includes the coach's message to parents is also filled with words of love from the boys.
Tech billionaire Elon Musk has sent a team of engineers to Thailand to see if they can help in the rescue effort.