The boys and their coach have been trapped in the cave system in the country's north for about two weeks.
The boys and their coach had been stranded in Tham Luang Nang Non since June 23 when they went exploring in the cave after a scrimmage. A massive worldwide search operation was launched and it took 10 days to locate the boys, who had taken shelter on a dry slope deep in the complex.
The first four boys, from the group of 13, including the coach, were rescued yesterday.
The extraction of those remaining is expected to take another two to four days, depending on conditions.
Divers took about four hours to escort Monday's fortunate four from the ledge to the chamber, the source added.
But he could not confirm if all five would come out today. The search and rescue operation has involved dozens of global experts and rescuers, including a USA military team. Billionaire Elon Musk dispatched a team of engineers, and President Donald Trump said Sunday the U.S.is working very closely with Thailand's military government on the rescue.
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.
Four boys were rescued on Sunday and they were judged as healthy as they recovered in an area hospital. Divers guided them though more than two miles of dark and narrow tunnels filled with murky water and strong currents.
A Reuters witness near the Tham Luang cave in the northern province of Chiang Rai saw medical personnel carrying four people out of the cave to waiting ambulances over the course of the day.
Authorities declined to say how many boys would be extracted on Monday.
The saga has dominated global headlines, with the team spending nine days unaccounted for inside the cave before British divers found the emaciated and dishevelled group huddling on a muddy bank.
Still, for the relatives of the Wild Boar team members, an agonising wait continued.
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But with oxygen levels inside dropping to risky 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.
A total of eight boys have now been brought out of the cave complex.
At least three more boys reached safety after diving and wading through channels of murky water, aided by expert divers, according to a rescue worker at the cave site.
The four boys rescued Sunday are recovering in a nearby hospital and are yet to see their parents.
One volunteer, former Thai Navy SEAL Saman Gunan, died Friday while placing spare air tanks along the escape route.
Thai authorities revealed that the first phase was executed "smoothly" and the boys who had been evacuated were in "good health". So far, their families have seen them through a glass barrier.
Authorities said a medical team was assessing whether to reunite the boys with their parents soon.
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. I've told Yod to get ready to take me out for fried chicken. They were in good condition in hospital, officials said.
Eight boys are still inside the cave and along with the team coach.
"On behalf of the United States, congratulations to the Thai Navy SEALs and all on the successful rescue of the 12 boys and their coach from the treacherous cave in Thailand".
A Royal Thai Police helicopter airlifts the fifth boy from a makeshift pad in Mae Sai district to Wing 416 in Muang district in Chiang Rai on Monday.