Information on the rescue operation, the health of those rescued - and their identities - has been tightly guarded by Thai authorities.
Interior Minister Anupong Paojina said the same divers who participated in Sunday's rescue are conducting the operation Monday because they are familiar with the cave conditions.
Last Friday, an ex-Navy SEAL died while placing oxygen tanks along the 4.7-kilometer (2.9-mile) evacuation route.
"Water levels are the same like the last two days", he said, adding that rescue efforts were expected to be "quicker or at least as quick as yesterday".
Each of the rescued boys has been guided through the dark winding cave by a pair of divers. Now, two boys along with their football coach remain in the caves.
"All five will be brought out at the same time today", he said, to cheers from reporters and rescue workers. They also anxious about dwindling oxygen levels in the cave.
They are still being quarantined from their parents because of the risk of infection and would likely be kept in hospital for a week to undergo tests, officials said. Medical experts say they are in high spirits and generally healthy.
The boys, ranging in age from 11 to 16 and their soccercoach set out to explore the cave on June 23, but became trapped after heavy rains flooded passages.
He added that the divers were the "same multinational team" that rescued the four boys on Sunday.
19 divers are said to be involved in the operation, which began at just after 10:00am local time.
Onlookers in Chiang Rai, Thailand, watch and cheer as ambulances transport some of the rescued schoolboys from a cave where they were trapped for two weeks.
The first eight boys rescued from a Thai cave are in decent physical and mental health with some even asking for chocolate, but they remain in hospital and under psychological observation for any lasting damage from their underground ordeal.
Mr Jesada said they were uncertain what type of infections the boys could face "because we have never experienced this kind of issue from a deep cave".
"The kids are footballers, so they have high immune systems", Jedsada told a news conference.
The emergence of the second batch of four on Monday evening was greeted with a simple "Hooyah" by the Thai Seals team on their Facebook page, an exclamation that lit up Thai social media. "Four plus one coach, so it's five".
In a series of tweets in the past few days, Musk chronicled the development of his custom-built mini-sub.
The third and hopefully final rescue mission is now underway.
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