Interior Minister Anupong Paojina said the same divers who participated in Sunday's rescue conducted the operation Monday because they are familiar with the cave conditions.
A total of eight boys have now been taken out of the Tham Luang Nang Non cave, according to the Thai navy SEAL group, which has a leading role in the rescue operation.
The 12 boys and their coach were trapped in the cave for two weeks.
Officials have yet to confirm the identities of the four boys freed, and Narongsak Osottanakorn, the head of the rescue operation, said their identities were being protected out of respect for the families of those still trapped inside the cave.
Witnesses say the boys freed Monday were treated at a make-shift hospital at the site, before being taken to a local hospital. But the rains stopped on Monday, and the mission resumed at 11 a.m. local time. Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days. Rescuers to take a break to place more air canisters along the underwater route to where the boys and their coach have been trapped since June 23rd.
As for the boys who have been rescued, they are in isolation and being monitored at a hospital for infection.More news: Trump arrives in Brussels ahead of potentially contentious North Atlantic Treaty Organisation summit
Four more young footballers and their coach at the Mu Pa (WIld Boar) Academy Mae Sai, Ekkapol Chantawong, are still on the ledge. Each of the rescued boys has been guided through the dark winding cave by a pair of divers.
Some of the boys have even asked for bread with chocolate spread - which they were given, said Jedsada Chokedamrongsook, the permanent secretary of the Thai Health Ministry.
UPDATE 0841 ET: The rescue operation has been suspended for the night in Thailand.
Getting all of them out the same way they came in was always a long shot, but so far one proving itself with two days of good news.
After his visit, he went to Chiangrai Prachanukroh Hospital to visit the rescued boys.
Though it rained again Sunday, it did not affect the water levels in the cave, said Narongsak Osatanakorn, the leader of the command center in charge of the rescue operation.More news: U.S. Working Closely with Thailand to Rescue Children from Cave
British, Australian, Chinese and Thai divers led them out, one tethered to each boy and one following from behind. Weather forecasters warned heavy rain could hit the area on Monday afternoon and continue through the week.
Family members have seen at least some of the boys from behind a glass isolation barrier, and Jesada said doctors may let the boys walk around their beds Tuesday.
The boys' nightmare experience - trapped in claustrophobic darkness by rising waters - resonated across the globe, riveting people both in Thailand and internationally who anxiously watched the news coming from this town along the border with Myanmar.
Authorities have said helicopters were ready to take cave evacuees to a hospital.
Thirteen foreign divers and five members of Thailand's elite navy SEAL unit are the main team guiding the boys to safety through narrow, submerged passageways that claimed the life of a former Thai navy diver on Friday.
The fate of the boys and their coach has gripped Thailand and drawn global media attention. "I'm quite emotional as a father - everybody has this feeling because we feel like it's our children who are inside the cave". We've got good news for you.More news: New Orleans Family Says Goodbye To Son In Unique Way
The cave complex is off-limits during the rainy season, which usually runs from May to October, when downpours can quickly flood it.