Chief of the rescue mission Narongsak Osottanakorn addressed reporters at the end of the 17-day mission, arriving at a media centre to a round of applause.
Operations to rescue a trapped Thai soccer team began on Sunday, resulting in four rescues. Two hours later, two more boys were extracted 10 minutes apart. It remains unclear how numerous boys have actually left the cave. Officials said the rescue could take four days to complete.
The 12 boys, aged between 11 and 16, and their coach, 25, went missing in Tham Luang Nang Non cave in northern Thailand's Chiang Rai Province on June 23.
Heavy rain and a lack of oxygen has made getting the boys out more urgent, and early this morning Thai Navy Seal divers safely traversed the 4km route with four of the boys - who are now recovering in hospital.
In addition to having no experience diving, the boys have mostly been without food and medicine for two weeks in tight quarters where oxygen is limited.
But monsoon flooding cut their escape and prevented searchers from finding them for 10 days. During the briefing, he said, "Today was the best situation - in terms of kids' health, water, and our rescue readiness".
Authorities have said helicopters were ready to take cave evacuees to a hospital.
Thai media identified the first boy to come out as Mongkol Boonpiem, 13.
"Clearly there is a huge risk of someone panicking if they are not used to the diving environment", Tony Haigh, a spokesman for the British Cave Rescue Council, which had two divers that found the boys, told the Post.
The first, almost 1km-long section from where the boys have been huddling in darkness is believed to be the most hard, requiring a long dive and crawling through mud and debris, with some crevices barely wide enough for a person.
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As night fell, the operation to rescue the remaining eight boys - some as young as 11 and weak swimmers - and their coach was called off until today.
Four boys were recently brought out of the cave and transported to a hospital.
On Friday, officials warned that oxygen levels in the cave dropped from 21% to 15%, further complicating rescue efforts. All the boys were in good condition, Narongsak said.
"I'm hoping for good news", he said.
"I mean, we're a big country and Thailand is a small country".
Families of the teenage soccer players have expressed their joy over the discovery of the boys.
The mother of one of the boys said she's sleeping at the cave site as she waits for confirmation that her son was pulled from the cave.
Why it is proving hard to extricate Thai cave boys What next?
Thai officials said Saturday they are anxious that heavy monsoon rain could soon make the job even more hard and they may need to quickly rescue the boys and the soccer coach from a partially flooded cave by helping them make risky dives to safety. Suggestions have included teaching the boys how to dive, and waiting until the waters subside.