Divers held the first four boys close to bring them out and each had to wear an oxygen mask, authorities said. Monday's arrivals from the Tham Luang cave were rushed to hospital in ambulances after spending more than two weeks trapped in the cave.
Thai officials have been tight-lipped about the rescue operation, and would not comment on how many people were removed Monday.
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.
Thailand's Meteorological Department said there was a 60 per cent chance of rain with more thunderstorms forecast throughout the week.
The same divers who took part in Sunday's rescue of four boys trapped in a flooded cave will also conduct the next operation as they know the cave conditions.
"We can only carry on the operation once we are ready and this will be done soon, because the air tank and other systems have to be reinstalled", he told reporters later.
Four boys and their 25-year-old coach remain in the Tham Luang cave, but Osatanakorn couldn't say whether they would all be rescued in the next mission.
Four more young footballers and their coach at the Mu Pa (WIld Boar) Academy Mae Sai, Ekkapol Chantawong, are still on the ledge.
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Ivan Karadzic, a Danish dive instructor who lives in Thailand and who was involved in the rescue effort of the four people on Sunday as a support diver, said late that night that "it went surprisingly well, we were expecting bad things to happen, and they didn't".
A relative of one member of the soccer team said that the boys' families had agreed to remain at the cave until all of the boys and the coach are brought out.
The rescued boys were being treated by medics at the field hospital, and were later airlifted to a larger nearby hospital.
Officials said it had not changed the water level in the cave but forecasters have warned rain could continue to hit the area throughout the week.
The eight boys who were rescued through Monday had to travel about two and a half miles with oxygen tanks and were accompanied by two professional divers each.
There were several concerns that prompted authorities to move forward with the plan to dive the boys out.
Rescuers are racing to beat the next rain, which could make their efforts more hard and unsafe. They were found alive last week by divers.
The football team went missing on June 23, having gone into the caves after Saturday practice to do some exploring, and ended up being trapped by rising flood water.