Narongsak said that there was no time limit on the rescue and that its progress would depend on weather and conditions inside the cave, but expected it to last through Monday.
Interior Minister Anupong Paochinda also said the boys were in good health.
He was taken by helicopter and ambulance to the same hospital in Chiang Rai where the first four boys rescued Sunday by a team of global and Thai dive experts are being treated. "We have set the plan for four people so if they want to take five out [at the same time], then they need to change the plan". They probably won't like enclosed spaces.
Rescued schoolboys are moved from a military helicopter to an awaiting ambulance at a military airport in Chiang Rai, Thailand, July 9, 2018.
The boys, who are in the Wild Boars soccer team, have captured hearts around the world as images of their smiling faces emerged from within the cave as they fought for their lives. The scheduled time was advanced from Monday night to race against time. "And we will do it faster because we are afraid of the rain".
Divers from Thailand and overseas, including the United States, China, Europe, and Australia have helped retrieve the boys, who are between the ages of 11-16.
They said the four boys already rescued are hungry but in good health in a hospital.
Four of the boys were safely rescued on Sunday after rescuers carried out a risky operation, amid fears the waters will rise again to a unsafe level.
Authorities have not confirmed the identity of the first four boys rescued.
"The water level has reached the lowest it has been in ten days". New oxygen tanks were being placed before the second stage of the rescue effort began.
With very few details released, parents of the remaining boys in the cave continued their agonising wait to be reunited with their sons.
The boys, some of whom don't know how to swim, have also been taught diving techniques to prepare them for their hard journey home. Relatives were able to see them through a glass partition, the governor said.
"We have not been told which child has been brought out".
A spokesman for Musk's Boring Co. tunneling unit, which has four engineers at the cave, has said Thai officials requested the device, which could potentially help the children through narrow, flooded cave passageways.
About 0.6 miles of the journey was believed to be underwater, requiring the boys to wear full face masks.
The reason a submarine of any size would be helpful to the rescuers is because exiting the cave requires negotiating long stretches under water, and some of the young Thai players do not know how to swim.
The first boy out was Monhkhol Boonpiam, 13, known as Mark.
Eight people remain trapped in the cave. The ambulance left the cave complex area hours after the start of the second phase of an operation to rescue a youth soccer team trapped inside the cave for more than two weeks. "They will not have to follow the normal schedules".
On Sunday, the Thai king led tributes to rescuers and the schoolboys as scenes of joyful weeping nationwide were shown on television. He said he expects some of them will suffer from post-traumatic stress disorder.
Getting to and from where the boys are has been an exhausting round trip, even for the experienced divers. "And we have more expertise than yesterday", he said.