Chiang Rai Gov. Narongsak Osatanakorn, who is heading the rescue effort, said earlier that Tuesday's operation began just after 10 a.m. and involved 19 divers.
Nargonsak said this phase may take longer than the previous two rescue missions, which both lasted several hours.
Chief of the rescue mission, Narongsak Osottanakorn, declined to comment on the identity of the four people brought out in the evening, saying updates would be supplied at a news conference that is scheduled to be held late on Monday.
Dr Richard Harris, 53, an anaesthetist from Adelaide, undertook the risky dive to reach the boys and their coach last Saturday, reported The Sydney Morning Herald.
Billionaire SpaceX founder Elon Musk tweeted at the weekend to say he was working with cave experts to build a mini submarine out of rocket parts that he thought could help a rescue effort to free 12 boys and their soccer coach trapped for weeks in a flooded underground cave complex in Thailand.
The ordeal of the Wild Boar football squad has gripped people in Thailand and all over the world, with cartoons expressing support for the team and rescue workers getting shared widely on social media.
Four were rescued Sunday and another four were rescued on Monday.
"It is certainly a risk and can take some time to manifest itself and make its presence known", said Andrew Watson, a specialist on rescues from mines and floods trapped.
"All eight rescued boys today are in good health, none have a fever", Jesada Chokedamrongsuk, permanent secretary of the ministry of public health, told a news conference in Chiang Rai in northern Thailand.
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Still, the four were undergoing medical checks in a hospital in Chiang Rai city, the provincial capital, and were not yet allowed close contact with relatives, due to fear of infections. The first and longest mission took 11 hours.
Two of the boys are thought to have lung infections, but there are no serious complaints to report.
"The kids are footballers so they have high immune systems", he added.
"They are diving in something considered (an) extremely hazardous environment in zero visibility, the only light that is in there is the torch light we bring our self".
Prime Minister Prayuth Chan-ocha was visiting all eight in the nearby hospital that they were helicoptered to, he said.
They were originally stuck after taking shelter from monsoon rains inside the caves, and walked further in to escape flooding.
The coach was in a weaker condition, having sacrificed his share of their meagre food supplies to give to the boys during the nine days before further help arrived.
It is understood that the British divers participating in the rescue specifically asked for Dr Harris' expertise. The sub, dubbed Wild Boar after the soccer team's name, is ready for use when and if necessary, Musk said in another tweet, adding that the vessel will remain in Thailand in case it's needed in the future.