Narongsak said that the "same multinational team" that went into the cave on Sunday to retrieve the first four boys was deployed on Monday. The four boys pulled from the cave Sunday in an urgent and risky operation that involved them diving through the cave's dark, tight and twisting passages were happy and in good health, authorities said.
The 12 boys, part of a youth soccer team known as the Wild Boars, first went missing with their coach more than two weeks ago. Spokesmen said the goal of the visit was "to give moral support to the rescue team members".
The second phase of the rescue effort began on Monday, hours after the first four were pulled to safety late Sunday.
Thai governor Narongsak Osottanakorn described the first rescue as "our masterpiece work" and claimed the four rescued boys were in "perfect" health - despite earlier reports that one was being "closely monitored". Officials had said before restarting the efforts that they hoped to have all nine people remaining in the cave rescued by the end of Monday local time.
But with oxygen levels inside dropping to unsafe lows and the prospect of heavy rain flooding the area completely, authorities decided they had to move quickly and take the group out through the water-filled tunnels.
He said that the decision to try to rescue the boys and their coach was made because conditions inside the cave were the best they could hope for and that water levels were low enough after days of good weather that it was possible to walk through long stretches of the passage.
Families have not been told which boys are free, so all parents have agreed to remain at the cave until the entire team is rescued.
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The names of the rescued boys were not released.
"This morning they said they were hungry and wanted to eat khao pad grapao", Narongsak said, referring to a Thai dish of meat fried with chili and basil and served over rice. The rescue operations were thereafter suspended for the day, CNN reported.
Monday's operation took nine hours, two fewer than Sunday, with rescuers helped by the experience they have accumulated, Narongsak told a news conference punctuated with rounds of applause.
The rescued boys were being treated by medics at the field hospital, and were later airlifted to a larger nearby hospital.
Rescuers had spent days balancing the risk of impending monsoons, which could have flooded the cave again, against the boys' readiness, weakened as they were by their ordeal.
The boys are being guided out of the cave by two divers with oxygen tanks.
The boys were flown by helicopter from the Tham Luang cave to the Chiang Rai Prachanukroh hospital, located at the heart of Chiang Rai province, about 70km (40 miles) away. So far, their families have seen them through a glass barrier.
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A former Thai Navy SEAL diver died in the cave last week due to lack of oxygen.
That makes for eight of the 13 people who have been trapped under increasingly unsafe conditions since late last month. Two of them possibly have a lung infection but all eight are generally "healthy and smiling", he said.
The boys brought out of the dark, winding cave on Monday are "safe and conscious", he told the media.
"I feel very happy, everybody is happy", said Hnin Jaiwong, the mother of one of the trapped boys, 13-year-old Sompong Jaiwong.
The cave complex is off-limits during the rainy season, which usually runs from May to October, when downpours can quickly flood it.
Eight boys rescued from cave in northern Thailand
The 12 boys and their coach were trapped after heavy rain in northern Thailand on June 23 but their rescue has now been completed. Musk posted photos on his Twitter account at around 5:00 a.m. local time Tuesday, reportedly from inside and outside of the cave.