The team's 25-year-old coach and four boys are still deep inside the flooded and sprawling cave.
British divers found the 13, hungry and huddled in darkness on a muddy bank in a partly flooded chamber several kilometers inside the complex, on Monday last week.
Rain had continued overnight but the governor's initial hope was that the third stage of the rescue could be performed faster than the rescues on Sunday and Monday, when four boys were freed on each day. Eight boys have been rescued so far while the remaining four boys and their coach still remained trapped in the cave.
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But with oxygen levels in their chamber falling to risky levels and complete flooding of the cave system possible, rescuers decided on the least-worst option of having divers escort them out through the extremely narrow and water-filled tunnels.
Describing the rescue operation's final phase, Narongsak said that divers were resting and replenishing air tanks - and hoping for good weather.
Why did rescuers take a 17-hour break after bringing out some of the boys?
"Today (Tuesday) we hope to be faster", Narongsak added, of the complex and risky operation that involves diving through narrow, flooded chambers.
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Jesada said the first four boys who were taken out are now eating well.
A Reuters witness saw three people being carried out of the Tham Luang cave on stretchers separately on Tuesday, the third day of the rescue operation. "We should learn from this experience to prevent it from happening again".
"All are safe" it added, signing off with a celebratory "Hooyah", a SEALs signature remark throughout the painstaking mission to get the boys out, AFP reported.
The boys appear to be in good health and their medical care is more of a precaution, CNN reports.
The team was trapped in a cave system after heavy rains forced them deeper into the caves in search of higher ground.
A nutritionist is monitoring their diet and has recommended that they eat nothing spicy or salty - despite the boys' cravings for spicy basil pork and rice and grilled pork. They were given a treat on Tuesday: bread with chocolate spread that they had requested. Two of them have a suspected lung infection and the group is still being quarantined from their parents because of the risk of infection.
But while divers risk their lives to get the team out, two Hollywood producers are beginning a project telling the boys's story.
Volunteers from as far away as Australia and the United States helped with the effort to rescue the boys.
But the head of the operation would not confirm whether all five could come out today, raising questions over whether coach Ekkapol Chantawong could be left behind to spend a lonely night in the cave.