The Thai Navy Seals leading the rescue operation have confirmed that eight boys in total have been extracted.
Four boys and their football coach remain inside the caves.
The group was trapped in the cave on 23 June after heavy rains caused flooding, and was found alive last week by divers.
Four boys were brought out safely on Sunday, but the mission was paused overnight for air tanks to be replaced.
Before the confirmation that four more boys had been rescued on Monday, air ambulances were seen departing from the cave system and ambulances arriving at the hospital in the nearby town of Chiang Rai.
Rescuers decided to go ahead with the operation to free the group because of fears that waters would rise again.
The rescue is complicated by sections in the cave involving diving – sometimes in a very confined space – and climbing.
Rescue mission chief Narongsak Osottanakorn said the operation had resumed at 11:00 local time (04:00 GMT) on Monday and would conclude at 21:00.
“More personnel” were being used than on Sunday, he added.
The names of the rescued boys have not been released out of respect for the families whose sons were still inside, and they have not been reunited with their own families, the mission chief said.
He said physical contact with loved ones would be avoided until a risk of infection had passed, though contact through glass or at a distance might be allowed.
Mr Narongsak allayed concerns that recent heavy rain might have raised water levels, saying conditions were “as good as yesterday”.
Rescuers took advantage of a break in the rain on Sunday to launch the mission earlier than some expected.
The first stage of the mission ran “smoothly” and the rescued boys were in “good health”, according to the Thai authorities.
How are the boys being moved?
A team of 90 expert divers – 40 from Thailand and 50 from overseas – has been working in the cave system.
They have been guiding the boys through darkness and submerged passageways towards the mouth of the Tham Luang cave system.
Getting to and from where the boys are has been an exhausting round trip, even for the experienced divers.
The process includes a mixture of walking, wading, climbing and diving along guide ropes already in place.
Wearing full-face masks, which are easier for novice divers than traditional respirators, each boy is being accompanied by two divers, who also carry his air supply.
The toughest part is about halfway out at a section named “T-Junction”, which is so tight the divers have to take off their air tanks to get through.
Beyond that a cavern – called Chamber 3 – has been turned into a forward base for the divers.
There the boys can rest before making the last, easier walk out to the entrance. They are then taken to hospital in Chiang Rai.
In an indication of how dangerous the journey can be, a former Thai navy diver died in the caves on Friday. Saman Gunan was returning from a mission to provide the group with air tanks when he ran out of oxygen.
He lost consciousness and could not be revived. His colleagues said they would “not let the sacrifice of our friend go to waste”.