A helicopter flew some of the boys to the nearby city of Chiang Rai where they were taken by ambulance to hospital.
A team of 13 global cave diving experts and five Thai divers entered the precarious cave system at 10am local time on Sunday, after attempts to drill through to them were abandoned.
"Now and in the next three or four days, the conditions are ideal [for evacuation] in terms of the water, the weather and the boys' health", said Narongsak, governor of the Chiang Rai province, where the caves are.
Authorities have been rushing to extract the boys, ages 11-16, and their coach from the cave as the annual monsoon bears down on the mountainous region in far northern Chiang Rai province.
Some took time on Sunday to pay tribute to Saman Gunan, a Thai Navy SEAL who died while trying to ensure the boys had enough oxygen.
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A source at the Chiang Rai hospital said that five emergency response doctors were awaiting the boys and a further 30 doctors were on stand-by. At the request of Thai authorities, Harris went into the cave yesterday to assess the boys and their coach before rescuers attempted the operation.
"The prime minister said that this kind of event should never happen again on Thai soil", Narongsak told reporters.
Water from heavy rains have flooded the cave, leaving the team trapped inside.
The boys were each being led by two divers as they went through 4km of pitch darkness, trudged through thick mud, clambered over slippery jagged rocks and dived through narrow passageways swirling with cold, strong currents.
The dramatic and risky rescue at the Tham Luang cave in the northern province of Chiang Rai was launched on Sunday and four boys were brought out that day.
The names of the four boys rescued from the caves last night have not been officially confirmed.
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.
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The Wild Boars and their coach became trapped on June 23 when they set out to explore the vast cave complex after soccer practice, when a rainy season downpour flooded the tunnels. Gen. Anupong said that process could take several hours.
A relative of one of the 12 boys, speaking to Kyodo News, compared Sunday's rescue to a miracle, adding that she wishes to see the remaining boys and coach get out soon.
It is still not clear how the boys will be rescued. They eventually found a dry landing spot, where they waited for nine days before being found by two British divers.
More rain is expected in the coming weeks.
"Football's Coming Home. First Wild Boars Out", a headline on one online Thai paper said on Monday, referring to a song chanted by English soccer fans at the World Cup now underway in Russian Federation. And many of them are experienced cave divers, which certainly helps because this is a very risky operation.
A frantic rescue mission was hatched in the week since they were found.
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