Workers have been laboring around the clock to pump water out of the cave, and authorities said Monday that heavy downpours overnight did not raise water levels inside.
The four boys pulled from the cave Sunday in an urgent and unsafe operation that involved them diving through the cave's tight and twisting passages were in good health.
Her husband Somboon said parents had been told they would not be able to visit their sons once rescued.
Earlier on Monday, divers placed new oxygen tanks along the way out of the underground network as part of preparations to repeat yesterday's mission.
Sunday night, teams of divers brought out four of the trapped boys to waiting ambulances.
The boys are said to be generally in good health but doctors are still evaluating whether they could have picked up any unsafe infections, such as the potentially lethal leptospirosis, while inside the damp cave for two weeks.
Narongsak said he's not sure if the remaining five people will be extracted in one or more operations.
Thai rescue team members walk inside a cave where 12 boys and their soccer coach have been trapped since June 23.
The perilous rescues have involved two divers accompanying each of the boys, all of whom have been learning to dive only since July 2, when searchers found them.
Rescue operation paused for 10 hours as teams prepare.
But Narongsak said earlier that mild weather and falling water levels over the last few days had created optimal conditions for an underwater evacuation that won't last if it rains again. Those conditions won't last if the rain resumes, he said.
The divers also brought out touching notes for the families written by some of the trapped boys.
The death Friday of a former Thai navy SEAL underscored the risks.
The operation to rescue the boys, ages 11-16, and their 25-year-old coach by having them dive out of the flooded cave began Sunday morning, with expert divers entering the sprawling complex for the complicated and risky mission.
Monsoon flooding cut off their escape route and prevented rescuers from finding them for nearly 10 days.
People around the world are following the developments in Thailand. The search and rescue operation has involved dozens of global experts and rescuers, including a US military team.
Elon Musk's Space X rocket company tested a "tiny kid-sized submarine" that could potentially help the children through the narrow, flooded cave passageways. The diver, the first fatality of the rescue effort, was working in a volunteer capacity and died on a mission to place air canisters along the passage to where the boys are, necessary for divers to safely travel the five- to six-hour route. "The war ends when we win all three battles - the battles to search, rescue and send them home". Medical staff involved in the rescue mission told Reuters their first assessments when the boys arrive at the hospital will focus on their breathing, signs of hypothermia and an airborne lung infection known as "cave disease" which is caused by bat and bird droppings and can be fatal if untreated and allowed to spread to other parts of the body.
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