The official declined to be identified as he is not authorised to speak to the media.
The boys have been trapped in the Tham Luang Nang Non cave since June 23 when they and their coach entered and were then cut off by flash flooding.
The group was found nine days later in a cramped chamber 2.5 miles inside the cave system by two British volunteer rescue divers.
Rescuers had planned to take a 10- to 20-hour pause in the rescue efforts to replenish the cave with oxygen and give the team of 18 divers leading the boys on the hard journey a chance to rest.
An update Saturday from the Thai navy said three navy SEALs were with the boys and their coach, one a doctor. "And we will do it faster because we are afraid of the rain".
It is understood the same divers who rescued the first four boys have been given the job of getting the remaining team members out.
Four boys were rescued on Monday evening following the four who were bought safely out of the cave on Sunday. They became trapped in the cave after heavy rain flooded the passageways inside.
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. Workers have been labouring around the clock to pump water out of the cave, and authorities said Monday that heavy downpours overnight did not raise water levels inside.
Interior Minister Anupong Paojinda told reporters the four boys rescued on Sunday were in good health in hospital but did not give details.
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There was no word on the condition of any of the people brought out on Monday.
Somboon Sompiangjai, 38, whose son Peerapat, known as Night, is still in the cave, said parents had been told they would not be able to visit their sons once rescued.
TRT World's John Joe Regan has the latest from Thailand.
One of the biggest concerns in the rescue operation is an area of the cave that is just 15 inches across so the boys have to separate from the divers in order to fit through.
Rescuers have been unable to extend a hose pumping oxygen all the way to where the boys are, but have brought them some oxygen tanks.
Phuwadech Kamnguen, a 14-year-old best friend of one of the trapped boys, said he's looking forward to eating KFC with the team again.
"The medical team is considering whether to let closest relative visit them", Osotthanakorn said.
Writing in elegant Thai script, the boys urged their parents not to worry, adding that they hoped they wouldn't get too much homework after being rescued and couldn't wait to eat their favorite foods again.
President Donald Trump tweeted yesterday: "The US is working very closely with the Government of Thailand to help get all of the children out of the cave and to safety".
As for the boys who have been rescued, they are in isolation and being monitored at a hospital for infection.
Narongsak said ahead of the rescue dive that recent mild weather and falling water levels had created optimal conditions for an underwater evacuation.