Four were rescued on Sunday and another four were rescued in a faster operation on Monday, after two weeks trapped in the cave complex in north-western Thailand.
"I insist that all 13 will be safe and sound", Chiang Rai provincial Gov. Narongsak Osatanakorn said at a news conference on Monday.
The Associated Press reports that the families of the boys "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".
Four other youngsters and their soccer coach are still inside.
Four more of the boys were carried on stretchers out of the cave on Monday, bringing to eight the total number brought out so far after two rescues in successive days. Anyone not essential to the mission had been ordered out of the cave, he added.
But bringing out the remaining four boys and their coach could take more than one operation, Narongsak warned.
The eight boys already evacuated from the cave over the weekend are being held in isolation - and aren't even allowed to hug their parents - as doctors assess them for histoplasmosis and other conditions.
They're all likely to stay the hospital for seven days due to their weakened immune systems, Chokedamrongsook said.
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By the evening, the boys were able to joke, laugh, and have normal conversation, doctors said. "The equipment they brought to help us is not practical with our mission", the publication also quoted him as saying.
The boys had asked for chocolate and bread, both of which the hospital had provided, he said. For the second group arrived last night, they are still wearing sunglasses.
Four were rescued on Monday, and the first four extracted on Sunday. One of the boys initially had a heartbeat that was too slow, and some had low white blood cell counts, but they have since been stabilized. "We've started giving them "medical food" this morning". "And we have more expertise than yesterday", he said.
Two boys and their 25-year-old coach remain in the cave.
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"The water level is still at a satisfactory level and we have enough teams to complete the mission", Narongsak said on Monday.
Thai policemen secure the road leading to Tham Luang cave area as rescue operations continue for those still trapped inside the cave in Khun Nam Nang Non Forest Park in the Mae Sai district of Chiang Rai province on July 9, 2018. The rescue effort is slowed somewhat by the fact that the team must replenish supplies and oxygen tanks that line the 2.5-mile route out of the cave.
The Thai rescue effort has been assisted by experts from around the world, and the death of a former Thai Navy SEAL diver who ran out of oxygen in the cave on Friday underscored the dangers of the mission.