The boys, ages 11-16, and their 25-year-old coach became stranded when they went exploring inside after a practice game.
The latest rescue operation began at about 10:08 am local time (1.08pm AEST).
Spicy Thai basil leaves on rice, or Pad Krapao, was the meal of choice for the four Mu Pa Academy football players after they were rescued from Tham Luang Cave on Sunday, rescue mission chief Narongsak Osottanakorn said on Monday.
In an atmosphere of growing confidence, close to jubilation, the rescuers said that, having rescued eight boys, they expected to bring out the final four boys later today.
Officials described the rescued boys as "hungry but happy".More news: Prince Harry treats Prince Louis to £8,000 christening present
4.27pm: The third day of the rescue mission has reportedly begun at 11am today (local time).
The rescue mission began on Sunday morning, almost a week since the 12 boys, aged 11 to 16, and their coach had been discovered on an embankment 2.5 miles (4 kilometers) inside the winding tunnels. They'll also be bringing back 3 Navy SEALS and a medic who have been in the cave with the team since the first day of the rescue efforts.
"Today (Tuesday) we hope to be faster", Narongsak added, of the complex and unsafe operation that involves diving through narrow, flooded chambers.
Thai officials say four boys were brought out of a flooded cave in northern Thailand on Monday.
Dr. Jedsada Chokedamrongsook, the permanent secretary of the Thai Health Ministry, said the first group of boys taken out on Sunday were aged 14 to 16. The 12 boys and their coach were trapped in the cave for two weeks. Relatives were able to see them through a glass partition, the governor said.More news: Hand of Fate 2 Officially Coming to Nintendo Switch; First Trailer Released
The authorites are still keeping the eight rescued boys away from their parents for fear of infection. The teams have risked their lives to deliver supplies and food to the children and their coach, and divers have been teaching the boys ― some of whom don't even know how to swim ― diving and breathing techniques to prepare them for their harrowing journey home. Crowds at the teeming rescue site cheer the good news, but attention soon turns to the hard task of getting the boys out safely.
Musk has offered a "kid-sized" submarine, named Wild Boar after the kids' soccer team, to help in the rescue operation.
The plight of the boys and their coach has drawn worldwide attention, with divers, engineers and medics among others flying in from around the world to assist.
VideoThe tech billionaire has developed a special submarine in case it needs to be used. Musk tweeted that the mini-sub was designed in such a way that it could safely make the trip, based on input from divers who had done it.
Three ambulances along with cars, hummers and soldiers have been seen entering the cave site where rescuers have been carrying out a high-stakes operation to bring out trapped members of a youth soccer team.More news: Wimbledon 2018: Clinical Novak Djokovic keen to take Centre stage
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