They are considering drilling a hole into the mountain to reach them if a water escape proves too risky.
The local governor supervising the rescue mission said Saturday that mild weather and falling water levels over the past few days had created appropriate conditions for an underwater evacuation, but that they won't last if it rains again.
If the risk from either the air or water increased "to the point that we can not accept, we will make decision", he said.
Rescue divers have since been able to take them food, oxygen and medical assistance, while a huge worldwide team works on a plan to free them.
They need good news he tells us. "When oxygen in our blood is low, more carbon dioxide will enter the blood stream".
Nick, Pipat Poti, 15: Mom, dad, I love you guys, and Toi too. I love you, mum and dad.
A letter from one of the boys inside the cave.
Coach Ekkapong Chantawong, 25: To all parents, the kids are alright now.
"From all the parents, please take care of all the children". I promise I'll care for them as best as I can. "I want to say thanks for all the support and I want to apologize to the parents".
The boys are also being trained in the basics of diving in case the floodwaters force authorities into a sudden evacuation through twisting and jagged passageways.
The rescue mission is proving to be hard for divers whose efforts are continually hampered by rising water that has filled sections of the cave, often forcing them to halt efforts.
In this Monday, July 2, 2018, file photo, a rescuer makes his way down muddy steps past water pump hoses at the entrance to a flooded cave complex where 12 soccer team members and their coach went missing in Mae Sai, Chiang Rai province, northern Thailand. When I get out I will go to eat. When they get out they want to eat many things. Relatives start to keep a vigil outside the cave.
Friday's death of the former SEAL underscores those risks. "If (there is) heavy rain and the situation is not good, we will try".
A team of more than 30 American military personnel from the US Pacific Command arrive, including pararescue and survival specialists. Even if they are given enough food to wait out the rainy season, there is no guarantee that the ledge they are sitting on will not be submerged.
The group became trapped deep inside the cave after flood waters gushed in.
However, Ivan Katadzic, a Danish diving instructor who has been ferrying oxygen tanks inside the cave, said after a dive on Friday evening he was "double positive" about the mission because the water level had dropped considerably. Drones are dispatched to help find new chimneys. "Everyone is a professional so we're trying to put it away and avoid it happening again", he said, adding: "Everybody is focusing on getting these boys out - keeping them alive or getting them out". But authorities said it remained unclear how long the boys would have to remain inside.
Officials have dismissed speculation that the boys could be trapped for up to four months, although supplies have been prepared for that period of time.
Osottanakorn admitted the rescue mission lacked the technology "to pinpoint where they [the boys] are staying".
Why it is proving hard to extricate Thai cave boys What next? They've practiced wearing diving masks and breathing, in preparation for the diving possibility.
A team of bird's nest collectors had scoured the mountainside for openings on Thursday.
Tragedy strikes: a diver helping to establish an airline to the boys dies after passing out while returning from the chamber. Crews are working to install a three-mile long oxygen tube and have delivered additional tanks to the boys. He warns the window of opportunity to free the youngsters is "limited", in the first official admission that they can not wait out the monsoon underground.
A scrawled message emerges from the coach of the team, offering his "apologies" to their parents.
Mr Chongklai Worapongsathorn, deputy director-general of the Department of National Park, Wildlife and Plant Conservation, said many holes have been drilled and many teams have been sent out to look for more, but so far, none of them can lead to where the boys are.