A crack team of foreign divers and Thai Navy SEALS has been guiding the boys out through almost 4 km (2.5 miles) of sometimes submerged, pitch-dark channels.
The head of the operation, Narongsak Osottanakorn, said a final operation would be "more challenging" because one more survivor would be brought out than the previous two operations, along with three Navy SEALs who have been accompanying them.
A senior public health official said separately that a medical team tending to the eight boys who have already been brought out from the cave has assured that they are in good health.
Rescue organisers say they need 20 hours to replan and replenish oxygen supplies, with the next rescue mission expected to come some time on Tuesday afternoon, weather permitting. Each operation has taken at least nine hours.
Two boys have minor lung infections and one had a fever, doctors have said.
The general leading the huge worldwide effort to rescue the young footballers and their coach thanked the god of rain for his forbearance, as the boys were guided out of the Tham Luang caves in full-face masks - easier than traditional respirators for novice divers to use - during an intense nine-hour operation. The group had gone for a trek when heavy rains trapped them in a dark, cramped chamber 2.5 miles inside in the Tham Luang Cave system. According to NBC News, the twelve boys, ages 11 to 16, and their 25-year old coach entered the caves two weeks ago but were trapped after rain caused flooding.
Four more members of a youth soccer team were pulled from a flooded cave in a second round of rescue operations in Thailand on Monday.
"Everyone is in high spirits and are happy to get out", Jesada added.
They are all likely to stay in hospital for seven days due to their weakened immune systems.
It was clear doctors were taking a cautious approach.
Their families were being kept at a distance because of fears of infection and the emaciated-looking boys were eating a rice-based porridge because they were still too weak to take regular food, authorities said. Relatives were able to see them through a glass partition, Narongsak said.
Four of the boys were safely rescued on Sunday after rescuers carried out a risky operation, amid fears the waters will rise again to a unsafe level.
Four ambulances and a convoy of other vehicles arrived at the cave site on Tuesday morning as rains hit the region.
The rescue missions take almost half a day to complete.
The rescue operation began over the weekend, and four boys and the coach still remain in the cave complex.
Chiang Rai acting Gov. Narongsak Osattanakorn said the second phase began at 11 a.m. and authorities "hope to hear good news in the next few hours".