Nine people remain trapped in the cave.
Narongsak Osatanakorn, the head of the joint command centre coordinating the operation said: "The factors are as good as yesterday ..." "We will have to do the next mission as successfully as the one we did today".
Officials have said storms forecast for Chiang Rai province in Thailand's far north had factored into their decision to go ahead with a complicated and unsafe plan for the boys aged between 11 and 16 and their coach to dive out of the cave.
It was not immediately clear Monday how the overnight rains had impacted water levels inside the flooded cave.
The second phase of the rescue effort began on Monday, hours after the first four were pulled to safety late Sunday. "We have to quarantine them for a little while due to fear of infection". Channel News Asia has also reported seeing ambulances carrying the sixth and seventh boys arriving at the Chiang Rai hospital. The rescued children were taken to the hospital, and officials said early Monday that they are strong and safe but need to undergo detailed medical checks.
He said the plan is to launch the third rescue mission within 20 hours, and he is hoping for "100 per cent success".
"They may show extremes in behaviors. they (may) sleep too much or have difficulty sleeping", says Aten, who is not involved in the boys' treatment.
Rescue teams had installed a static rope along the dive path, giving the boys a guide, and experienced divers were reportedly positioned at various points along the way for assistance.
Officials said the boys freed Sunday were hungry but in good health, and had asked for holy basil stir-fried rice, a popular Thai dish.
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When it was realised that the boys were in the cave system, divers began the process of trying to find them in the enormous area. The device could be used to rescue one boy at a time as it has space to fit in one person with his arms crossed, he said.
But the death of a former Thai Navy SEAL diver who ran out of oxygen in the cave on Friday underscored the danger of the journey.
But Narongsak said earlier that recent mild weather and falling water levels had created optimal conditions for an underwater evacuation. Those conditions won't last if the rain resumes, he said.
That led an upbeat Narongsak to promise more "good news" on Monday afternoon that materialised a few hours later with the emergence of the other four.
The oxygen ports and nose cone fitted to the device would prevent damages when it comes in contact with rocks, he said.
Sunday's mission involved 13 foreign divers and five Thai navy SEALs.
The boys and their coach, whose team is known as the Wild Boars, became stranded when they were exploring the cave after a practice game on June 23.
Rescuers are moving ahead quickly because they are afraid monsoon rains will completely flood the caves. More than 1,000 journalists from across the world have descended on northern Thailand to report the story. The Daily Telegraph is reporting that the sixth was rescued just two hours later.
Divers held the boys close to bring them out, and each had to wear an oxygen mask to enable normal breathing, authorities said. The images showed a team of SpaceX engineers testing the device in the swimming pool of a Los Angeles high school.