An ambulance carrying one of the boys rescued from the Tham Luang cave network on Sunday.
Thailand's Meteorological Department said there was a 60 per cent chance of rain with more thunderstorms forecast throughout the week.
Air tanks were planted along the route earlier on Monday.
"The mission has resumed", a government official closely involved in the mission told Reuters, declining to be identified.
The boys and their coach had been stranded in Tham Luang Nang Non since June 23 when they went exploring in the cave after a scrimmage. Divers guided them though more than two miles of dark and narrow tunnels filled with murky water and strong currents.
Lastly came Pipat Bodhu, 15, aka Nick, who was not even in the team but came along as a friend of the goalkeeper.
Chiang Rai acting Gov. Narongsak Osatanakorn, who is heading the rescue, had said the second phase began at 11 a.M. Monday and authorities "hope to hear good news in the next few hours". Four boys and their football coach are still trapped inside the cave.
Narongsak said that the "same multinational team" that went into the cave on Sunday to retrieve the first four boys was deployed on Monday.
The president of soccer's governing body, FIFA, has invited the boys to the World Cup Final in Moscow on Sunday if they make it out in time.
He was taken by helicopter and ambulance to the same hospital in Chiang Rai where the first four boys rescued Sunday by a team of worldwide and Thai dive experts are being treated.
Workers have been laboring around the clock to pump water out of the cave, and officials said Monday that despite heavy downpours overnight, water levels inside the cave did not rise.
Interior Minister Anupong Paojinda told reporters the four boys rescued on Sunday were in good health in hospital but did not give details.
While the governor would not confirm the identities of the four boys, he said the first one emerged at 5:40 p.m. local time (6.40 a.m. ET), followed by the second boy 10 minutes later.
The rescued kids are now in the hospital, where they should receive the proper care before being released to their families.
Sunday's rescue mission was described as a success by Thai officials.
"This morning they said they are hungry, and they wanted phad kra pao", he said.
Narongsak said the rescued boys had not been identified out of respect for the families whose sons were still trapped, adding that the boys were being kept away from their parents due to fear of infection.
"We expect that if there is no unusual condition. the 4 boys, 1 coach, the doctor, and 3 SEALs who have been with the boys since the first day will will come out today", he told a press conference to loud cheering.
Narongsak said ahead of the rescue dive that recent mild weather and falling water levels had created optimal conditions for an underwater evacuation.
Rescuers have been rushing to extract the boys, ages 11-16, and their 25-year-old coach from the cave as the annual monsoon bears down on the mountainous region in far northern Chiang Rai province.
At least nine ambulances loaded with stretchers and blue oxygen tanks waited by the mouth of the cave on Monday. The mood was fairly relaxed among the soldiers, medics, engineers and volunteers in yellow shirts that milled around.
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