The local governor in charge of the mission to rescue them said Saturday that cooperating weather and falling water levels over the last few days had created appropriate conditions for evacuation, but that they won't last if it rains again.
"I confirm that we are at war with water and time from the first day up to today", said Narongsak.
He says floodwaters have been drained as much as possible, "but if it rains and adds to it again, we don't know what other risk factors we will have to face".
Officials say an oxygen line has been installed to counteract the increased carbon dioxide that comes from so many people breathing within such a small area.
The letters provoked a surge of emotion from families, who first endured nine long days before their children were found dishevelled and emaciated but alive on Monday - and now face an agonising wait for a unsafe evacuation.
The boys, aged 11-16, and their 25-year-old coach were missing for over a week before rescue divers finally found them on Monday.
"The SEAL team takes very good care of us", wrote Panumat "Mix" Saengdee, 14.
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"Thank you all for the support", the coach wrote.
The distressed parents of a group of Thai boys trapped inside a cave have reportedly sent them letters after authorities confirmed they're not strong enough to dive, so can't be rescued yet. But don't worry. But don't forget my birthday.
One of the boys, identified as Tun, wrote: "Mum and Dad, please don't worry, I am fine".
The boys, whose letters to their parents from inside the cave were published on Saturday, were still in good shape.
Don't worry. I miss everybody, Grandfather, Auntie, Mom, Dad and brothers. "I love you", wrote 11-year-old Chanintr Wiboonroongruang (Titan).
The boys were exploring the cave when they and their football coach became trapped by rising waters on 23 June. Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days.
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Despite the unfortunate death, the volunteers have vowed to continue providing the boys with oxygen as the planned extraction, which involves the boys swimming out of the cave with divers, could still take months.
Earlier Friday, Thai SEAL commander Arpakorn Yookongkaew said there is a "limited amount of time" to rescue the boys and the coach.
The risks were underlined by the death on Friday of a former Thai military diver Saman Kunan, who ran out of oxygen while returning from the chamber where the boys are trapped.
It was too risky to leave the boys much longer, Yoo-kongkaew said, despite the risks involved in attempting to bring them out.
"Now and in the next three or four days, the conditions are flawless [for evacuation] in terms of the water, the weather and the boys' health", said Mr Narongsak, governor of the Chiang Rai province, where the caves are.
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