Four boys and their soccer coach remain in the cave.
The eight boys rescued after being trapped for more than two weeks were described as generally healthy.
All eight boys rescued on the first two days are being treated in an isolation ward in a Chiang Rai hospital.
Citing a former SEAL diver with the Thai Navy, the BBC reported that some of the boys were asleep, while others were "groggy".
All organisations taking part in the rescue mission would elaborate on their rescue operations in another press conference at the same place Wednesday night, Mr Narongsak said.
Rescued schoolboys are moved from a military helicopter to an awaiting ambulance at a military airport in Chiang Rai, Thailand, July 9, 2018.
The dry weather allowed workers to pump nearly a foot of water from flooded portions of the cave to help in the complicated and risky rescue. The other four and their 25-year-old coach remain trapped where they have been for more than a fortnight after heavy rains flooded the cave system.
"It is certainly a risk and can take some time to manifest itself and make its presence known", said Andrew Watson, a specialist on rescues from mines and floods trapped.
Last week, Musk tweeted that he was sending a team of SpaceX and Boring Company engineers to Chiang Rai in northern Thailand on Saturday to help rescue efforts, supplying technology such as Tesla Powerwall batteries and pumps for removing water.
"When the first group came, their temperatures were low", he said. They will be monitored closely to see if they pick up any infectious disease from deep within the cave.
Besides being developed as a learning centre, there were also plans by the authorities to turn the cave into a museum where efforts to compile equipment and tools used during the massive operations had already begun, he said. The extraction started on Sunday and eight of the children have been successfully brought out. "I would like to see the love and cooperation over the past 17 days continue for the sake of national development", he said.
Writing in elegant Thai script, the boys urged their parents not to worry, adding that they hoped they wouldn't get too much homework after being rescued and couldn't wait to eat their favorite foods again.