But the first of the four boys emerged from the cave entrance about nine hours after a team of 18 worldwide cave diving experts went in to retrieve them.
The operation on Monday went more smoothly than on Sunday and took two hours less as the practice became more refined, he said. Their condition was not immediately clear.
The next operation will begin in 10 to 20 hours and will involve 90 divers, he said.
Two ambulances left the cave and drove to a nearby helipad, and a helicopter was seen taking off.
While the governor would not confirm the identities of the four boys, he said the first one emerged at 5:40 p.m., followed by the second boy 10 minutes later.
The mission was only launched on Sunday morning because floodwaters inside the cave were at their lowest level in days.
The plan was attacked as too risky, but fearless rescuers forged ahead to save the first four of 12 boys trapped in a Thai cave as torrential rains hit the region.
The death of a former Thai Navy SEAL diver who ran out of oxygen in the cave on Friday underscored the danger of the journey even for professionals. For the last several days, crews have been trying to drain enough water out of the cave to make the rescue easier. The path out is considered especially complicated because of twists and turns in narrow flooded passages.
Applause erupted as Mr Narongsak said he had met the children and their health is "perfect".
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The names of the rescued boys were not released.
Osotthanakorn said the rescued boys would stay isolated to ensure that they were healthy, but that they had a strong appetite, and were asking for a Thai dish of beef with basil and chili.
Monsoon rains flooded the cave preventing the team from getting out. Apart from the Thai authorities, 19 Australian divers are a part of the unsafe rescue mission.
President Donald Trump said in a tweet on Sunday: "The U.S.is working very closely with the Government of Thailand to help get all of the children out of the cave and to safety. Very courageous and talented people!"
The incoming monsoon will only cause water levels to rise, further jeopardizing the lives of those who remain trapped inside of the Tham Luang cave complex. Earlier efforts to pump water out of the cave have been set back by heavy downpours. I can not order them around. This what we have been racing against since day one. They were found more than a week later, stuck on a small muddy patch deep in the cave's network of chambers. The boys sounded calm and reassuring in handwritten notes to their families that were made public Saturday. Ten of the worldwide divers started the treacherous journey into the mountain, with the remaining three following four hours later at 2pm to operate as fresh back-up divers in the event of a crisis. "I had been anxious about my son, that he would be exhausted, he would be tired", he said. Grandpa, Uncle, Mom, Dad and siblings, I love you all. "Love you all", wrote Mick. It looks like people are leaving this site for the night.
The lack of space has added complexity to storing enough canisters of oxygen along the route out. Another, of indistinct origin, asked their teacher not to give them a lot of homework. The letter shows the boys in good spirits despite their ordeal.
"I'm hoping for good news". "I want to say thanks for all the support and I want to apologise to the parents".
But the survival of those remaining in the cave is far from guaranteed with extraction efforts put on hold until Monday morning to allow rescue divers time to resupply.
Their plight transfixed Thailand and the rest of the world, as authorities struggled to devise a plan to get the boys - aged between 11 and 16 - and their 25-year-old coach out.