The three-week ordeal started on June 23 when rising flood waters trapped the soccer team inside the cave with no way out.
The four boys rescued first are "well, they're up and about", Sky News' southeast Asia correspondent, Siobhan Robbins, said.
They lost weight during their ordeal, but had water while they were trapped and are in good health, an official said on Wednesday.
Even so, all need to be monitored in the hospital for seven days and then rest at home for another 30 days, he said. Doctors were anxious about potential infections the children could have contracted in the cave.
Members of the "Wild Boars" soccer team, who range in age from 12 to 16, and their coach became trapped after a rainy season downpour turned a cave adventure in the northern province of Chiang Rai into a nightmare, flooding the tunnels and making it impossible to leave.
"It might be because they were all together as a team", public health ministry inspector general Thongchai Lertwilairatanapong told reporters.
However, Prime Minister Prayuth Chan-ocha has said precautions would have to be implemented both inside and outside the cave to safeguard tourists. "When I visited them, I also told them to be good citizens".
Authorities held a press conference early Wednesday in Chiang Rai to discuss the boys' continued recovery from a variety of minor ailments.
After a 17-day struggle, an image of the Thai boys flashing victory sign, smiling and waving from their hospital beds gripped the world.
The most unsafe part of the journey out of the labyrinthine cave system was the first kilometer, during which they were required to squeeze through a narrow flooded channel.
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The group was led out in three batches by a team of 13 global divers flanked by Thai Navy Seals, who greeted each successful rescue with a "Hooyah" on their Facebook page.
Narongsak, giving details of the rescue, said falling oxygen levels inside the cave complex had added a sense of urgency.
"I want to say thanks to those who rescued my boy".
Here are some of the heroes who took part in the rescue mission. "For SEALs, this is what we were trained for".
The four boys rescued on Sunday are now eating normal food and walking around, while the four extracted on Monday are being given soft food.
The rescue has dominated front-page headlines in Thailand and beyond for days.
"All Wild Boars Saved", read one headline.
The fate of the boys has even resonated as far as Russian Federation, where soccer's World Cup is reaching its final stages.
It went viral, earning more than 9,000 retweets in less than a day.
At least three of the boys in the team as well as their coach are stateless refugees and might have restricted travel rights, Reuters has reported.