Four ambulances were seen leaving the Thai cave site Monday.
Rescue operations on Monday were expected to end by 9 p.m. local time.
Medics appeared to remove one person on a stretcher but hid the person's identity behind multiple white umbrellas.
Mr Narongsak allayed concerns that recent heavy rain might have raised water levels, saying conditions were "as good as yesterday" "We should hear good news again", he added.
The second group of four rescued on Monday are aged 12 to 14. That brought the total number of boys rescued to five.
Having completed this section, the boys are then handed over to separate, specialist rescue teams, who help assist them through the remainder of the cave, much of which they can wade through.
In this undated photo released by Royal Thai Navy on Saturday, July 7, 2018, Thai rescue teams arrange water pumping system at the entrance to a flooded cave complex where 12 boys and their soccer coach have been trapped since June 23, in Mae Sai, Chiang Rai province, northern Thailand. It ended with their fighting cheer, adopted from the U.S. Navy: "Hooyah!".
Authorities spent hours replenishing air tanks along the cave's treacherous exit route.
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.
Divers held the first four boys close to bring them out and each had to wear an oxygen mask, authorities said. They were able to make recommendations on things like changing cabling layout and adjusting the flow of hoses to improve pumping power.
The unidentified boys were carried out of the Tham Luang Nang Non cave on stretchers and into ambulances Monday before being airlifted to the Chiang Rai Pranukroh Hospital. Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days.
So far, rescues have been spaced out to allow for the divers to rest and the oxygen tank to be restocked.
Narongsak said Saturday that experts told him new rain could shrink the unflooded space where the boys are sheltering to just 10 square metres (108 square feet). "The divers that were assembled from many countries are proud to have conducted this operation until its success", Narongsak said. "Some others are preparing for the next operation". To get the remaining boys out, divers will be forced by the narrow passages to accompany them one at a time.
"It's very likely that while the boys were in the cave but not yet discovered by rescuers that they experienced various degrees of anxiety, fear, confusion, vulnerability and dependency, and perhaps hopelessness", said Paul Auerbach, of the Department of Emergency Medicine at Stanford University's medical school. A retired Thai Navy SEAL assisting with the operation died Friday after running out of oxygen, underlining the danger of the rescue. Two divers were assigned to each child to help them navigate the unsafe, narrow passageways. The other, and perhaps more worrying, was that oxygen levels in the complex were falling close to unsafe levels.