Thailand's Interior Minister Anupong Paojinda has revealed the same divers who rescued the four boys will also conduct the next operation due to their knowledge of the terrain. But a father of one of the boys told Reuters parents "can't visit our boys in hospital" and that "we have not been told which child has been brought out". Eight others, plus their coach, remained in the cavern.
The head of the rescue mission, Narongsak Osottanakorn, said last week they would bring the fittest people in the group out first.
"I feel very happy, everybody is happy", said Hnin Jaiwong, the mother of one of the trapped boys, 13-year-old Sompong Jaiwong. "If something changes, we will stop but we expect the operation will finish in a couple of days", he said.
The diving team needed 10-20 hours to recuperate following the first operation. "Today is D-Day", he told reporters, saying the group was mentally and physically prepared.
Heavy monsoon rains lashed the mountainous Chiang Rai region, where the Tham Luang Nang Non cave is situated, for several hours overnight on Sunday. A Thai army commander said the entire operation could take up to four days.
More than 100 exploratory holes were also bored - some shallow, but the longest 400 metres deep - into the mountainside in an attempt to open a second evacuation route and avoid forcing the boys into the risky dive.
"If we are asked to send more of course we will, but we are part of an worldwide response group working under the guidance of the Thai government and the Thai navy", Ms Bishop said.
It was a feat that, even two days earlier, they had said was impossible.
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Billionaire tech developer Elon Musk had also offered to provide assistance, in the form of a "kid-size submarine", which could arrive in Thailand early Monday, local time. A former Thai Navy SEAL passed out making the dive on Friday and died.
The high-risk rescue dive began with a sense of urgency after authorities failed to settle on an alternative means of bringing the boys out. But authorities became anxious in recent days as oxygen levels inside the cave dropped because of the presence of a high number of rescue workers.
Millions of gallons of water have been removed from the caves in the last week in an attempt to make it passable for the rescuers and the trapped football team.
Volunteers and support team members applaud as a diver leaves the cave after a successful mission on Sunday.
In all, 13 foreign divers and five Thai SEALS are involved in the rescue, which requires a treacherous, 2.4-mile journey through the cave complex.
Relatives say the boys had been inside the cave during the dry season, when the labyrinthine complex is easier to navigate.
The rescue mission is proving to be hard for divers whose efforts are continually hampered by rising water that has filled sections of the cave, often forcing them to stop. The American team of 30 people at the site includes 17 Air Force search-and-rescue specialists.