Narongsak said he was not sure if the remaining five people will be extracted in one or more operations.
So far, rescues have been spaced out to allow for the divers to rest and the oxygen tank to be restocked. The four evacuated on Monday were also hospitalized, although their condition was not announced.
The rescued children were taken to the hospital, and officials said early Monday that they are strong and safe but need to undergo detailed medical checks.
The unsafe bid to rescue the boys - aged between 11 and 16 - resumed after a break on Sunday night to replenish oxygen supplies and make other preparations deep inside the cave complex in northern Thailand's Chiang Rai province.
Officials suspended the rescue operation on Monday, after pulling an eighth boy from the cave, leaving four boys and their coach still inside.
The remaining nine boys are still at the location where divers had found them about 500 metres from the so-called Pattaya Beach. The Thai authorities have been pumping out water from the cave system ever since locating the missing soccer team, but that wasn't enough to remove all the water. And while oxygen is placed along the road, one experienced ex-Thai Navy SEAL diver lost his life last week while replacing the oxygen canisters.
"All conditions are still as good as they were yesterday", Chiang Rai acting Gov. Narongsak Osattanakorn said, as relayed by the AP.
"Living in a cave has a different environment, which might contain animals that could transmit any disease", they said.
Officials called the four boys who have already been rescued, "hungry, but happy".
The potential for rising water and the dwindling oxygen levels added to the urgency of getting the team out. Efforts to pump water out of the cave have been set back by heavy downpours.
An ambulance transports the fifth boy rescued from Tham Luang Nang Non cave to hospital on July 9, 2018 in Chiang Rai, Thailand.
Monsoon flooding cut off their escape and they have been on a rocky shelf inside a cave chamber since. More than 1000 journalists from across the world have descended on northern Thailand to report the story.
Dozens of foreign divers and other experts from around the world were brought in to help the rescue effort, working alongside the Thai Navy SEALs.
Omar Reygadas, who spent 69 days trapped underground in Chile in 2010 with 32 other miners, said faith and prayer, as well as humour were very important to the miners at times when they doubted they would get out.