An Australian doctor, a diving expert, gave the final approval on the health of the boys - clearing the way for the rescue.
Earlier the first two schoolboys emerged from the cave after divers launched a daring and risky mission to rescue the children and their soccer coach, who have been trapped underground for more than two weeks.
One of the boys to emerge was a 13-year-old Mongkol Boonpiem, local media has reported.
The group became trapped on June 23 when they started exploring the caves after going on a picnic following football practice. They are then taken to hospital in Chiang Rai.
They said a combination of the weakest and the strongest boys had been selected to attempt yesterday's perilous operation.
The dozen boys between the ages of 11 and 16 are accompanied by their 25-year-old coach.
The cave system, in a limestone mountain range bordering Myanmar in northern Thailand, has proven to be a formidable challenge for the global rescue coalition drawing some of the world's best divers who have volunteered to help in the operation alongside Thai Navy SEALs.
The outgoing Chiang Rai province Governor Narongsak Osottanakorn in charge of rescue operation called the worldwide divers "all-stars" and the Thai divers "five of our best". The Thai official in Sunday night's news conference said rescue workers need "about 10 hours" to prepare for next operation.
Those still inside the cave are perched on a small muddy ledge four kilometers (2.5 miles) inside the cave complex, surrounded by flood water and with a limited supply of oxygen.
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Rescuers part of the Thai navy SEAL partaking in the operation posted on Facebook showing hands locked with a caption vowing to bring the boys home. "Finding the boys doesn't mean we've finished our mission".
The rescue mission could take two to four days depending on the conditions in the cave.
Who are the boys and their coach?
The group had been missing for nine days before they were found huddled inside the cave.
Officials had looked at many different ways to save the boys and their coach.
The team of 12 boys and their coach entered the cave system on June 23, but torrential rain caused the water level within the cave to rise rapidly, forcing them to venture deeper. At 9pm on Sunday, four boys had been evacuated from the cave.
Meanwhile rescuers fed a kilometres-long air pipe into the cave to restore oxygen levels in the chamber where the team was sheltering with medics and divers.
Elon Musk wrote on Twitter that engineers from two of his companies, the aerospace manufacturer SpaceX and the tunnel-construction company Boring Company, were headed to Thailand to lend their assistance. It was not immediately known if a US diver was among them.