Eight have been rescued so far in an operation that began on Sunday.
"All eight are in good health, no fever. everyone is in a good mental state", Jesada Chokedamrongsuk, permanent secretary of the public health ministry, told reporters on Tuesday at Chiang Rai hospital in the clearest update on their condition so far.
Four boys were rescued on Monday, joining the first four boys who were extracted Sunday evening in the hospital. "Now they are fine", he said. Another five still await rescue, including the team's 25-year-old coach.
"We have more expertise than yesterday", he said.
Narongsak said after the first four boys were rescued that they would be quarantined "for a while because we are concerned about infections". "Cave diving requires a lot of training, and it's still unsafe even for the best cave divers".
Four more of the boys trapped in a flooded underground cave have been successfully rescued in a second day of hazardous underwater diving.
1 NEWS' Kimberlee Downs has the latest from Chiang Rai.
It was expected to end by 9pm local time, he said.
Ambulances and a helicopter were seen rushing from the cave site on Monday.
In total, 13 foreign cave divers and five Thai navy SEALs participated in Sunday's rescue, according to Reuters.
"This morning, they said they were hungry and wanted to eat khao pad grapao", he said, referring to a Thai dish of meat fried with chili and basil, and served over rice.
All four were airlifted to a hospital in the nearest city, Chiang Rai.
The leaders overseeing the desperate and risky rescue of 12 young soccer players and their coach from a flooded cave labyrinth in northern Thailand were only half joking when they quipped that success was in the hands of the rain god Phra Pirun. A massive global search operation was launched and it took 10 days to locate the boys, who had taken shelter on a dry slope, deep in the complex. Rescue operations have halted for the night and will restart on Tuesday.
The rescue missions take almost half a day to complete.
Monday's mission involved 18 divers from Thailand and overseas. Narongsak on Monday said their identities were being protected out of respect for the families of those still trapped inside the cave. "We believe that we can do even better and it will be a 100 percent success", he said. 4.24pm: The rescued boys have been set up with IV drips and antibiotics, as well as receiving vaccines for tetanus and rabies, the Guardian reports.
They were found last Monday by two expert British divers.
The death Friday of a former Thai navy SEAL underscored the risks. However, they ended up starting the rescue effort a few hours earlier than planned.
There were several concerns that prompted authorities to move forward with the plan to dive the boys out.