Thais have been fixated on the crisis, hoping desperately for the safe return of the 12 boys and their 25-year-old football coach, after they ventured into the Tham Luang cave complex after practice and became trapped by rising waters more than a fortnight ago.
It was unclear what time the rescue effort would resume on Tuesday, with operations chief Narongsak Osottanakorn telling reporters divers had crafted plans to extract four people at a time.
Nargonsak said this phase may take longer than the previous two rescue missions, which took up to 11 hours.
Families have not been told which boys are free, so all parents have agreed to remain at the cave until the entire team is rescued.
The search and rescue operation has riveted people in Thailand and internationally, with journalists from across the globe traveling to this town along the border with Myanmar to report on the ordeal. His colleagues said they would "not let the sacrifice of our friend go to waste".
Thai authorities said the first four rescued Sunday have been kept in quarantine until the risk of infection subsides.
A crack team of foreign divers and Thai Navy SEALs guided the boys during a nine-hour operation through almost 4 km (2.5 miles) of sometimes submerged channels from where they have been trapped for more than a fortnight.
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Heavy monsoon rains lashed the mountainous Chiang Rai region, where the Tham Luang Nang Non cave is situated, for several hours overnight on Sunday.
Rescued schoolboys are moved from a military helicopter to an awaiting ambulance at a military airport in Chiang Rai, Thailand, July 9, 2018.
The boys, whose names have not been revealed, are being treated at Chiang Rai Prachanukraw Hospital in Muang district.
The rescue missions take almost half a day to complete.
"We expect that if there is no unusual condition. the four boys, one coach, the doctor, and three SEALs who have been with the boys since the first day will come out today", he told a news conference to loud cheering.
The safety of the divers, who have meticulously planned the mission, is also paramount. "We believe that we can do even better and it will be a 100 percent success", he said. Highlighting the extreme dangers, a former Thai Navy SEAL died Friday while replenishing the oxygen canisters laid along the route. Add Thailand Cave Rescue as an interest to stay up to date on the latest Thailand Cave Rescue news, video, and analysis from ABC News.
Some divers rescuing the boys trapped in a cave in northern Thailand have traversed about 10 miles (16 km) over the past two days. More worrying, however, oxygen levels in the cave were falling.