The second rescue involved numerous same divers who evacuated the first four boys Sunday, former Chiang Rai governor Narongsak Osotthanakorn told reporters.
On Sunday, officials waited until several hours after the rescued boys had been transported to hospitals to announce their rescue.
The same elite divers involved in Sunday's rescue would conduct the next one, given their knowledge of the cave conditions, Thailand's interior minister said in a statement.
The Thai Navy Seals said in a Facebook post just before 10pm yesterday, "Tonight, we can sleep well", as the Day 1 rescue operation came to a close.
The billionaire entrepreneur has been tweeting proposals and offering his services to the Thai government in its efforts to extract the 12 boys and their soccer coach from a partially flooded cave. Monday's mission involved 18 divers from Thailand and overseas.
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.
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 first four boys rescued from the cave are apparently now recovering well in hospital, demanding bowls of fried rice. His colleagues said they would "not let the sacrifice of our friend go to waste".
Leicester City winger Riyad Mahrez undergoes Manchester City medical
It is understood that Mahrez has been given permission by Leicester to stay at home and continue his own personal training programme.
He said the plan is to launch the third rescue mission within 20 hours, and he is hoping for "100 per cent success".
The boys are being guided out of the cave by two divers with oxygen tanks. Onlookers were seen watching and cheering as they drove by.
However, after news of the rescue of four boys emerged, Musk tweeted, "Hopefully useful".
Officials lavished praise on the Thai and worldwide divers who executed the unsafe rescue mission, guiding boys who can barely swim and have no diving experience through a treacherous 4-kilometer-long (2 1/2-mile) escape route that twisted and turned and rose and fell inside the mountain cave complex.
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. Four boys and their coach remained inside the cave. A frantic rescue mission was hatched in the week since they were found.
UPDATE 0841 ET: The rescue operation has been suspended for the night in Thailand. And while oxygen is placed along the road, one experienced ex-Thai Navy SEAL diver lost his life last week while replacing the oxygen canisters. Musk said his submarine has eight handles, four in the front and four in the rear, and four air tank connections. Health officials say the rescued boys will be hospitalized for at least seven days, but they have been cleared to eat normal food.
Soldiers arrive outside the Tham Luang cave complex in the northern province of Chiang Rai, Thailand, July 8, 2018. To get the remaining boys out, divers will be forced by the narrow passages to accompany them one at a time.
"The Prime Minister wants this to be a lesson, this should not happen again in Thailand", Narongsak said.