The earliest any members of the group could emerge would be 9pm (2am NZ time).
Narongsak Osottanakorn, head of the operation, said crews will do everything they can to minimize the risk.
A heavy rain shower hit northern Thailand overnight, worsening conditions at the cave where rescuers were waging a "war with water and time".
There has been speculation mounting for some hours that the rescue operation is imminent, if not already under way.
A press conference is scheduled for today.
The oxygen tanks are needed because levels are dropping down to an alarming 15 percent.
"It's about rain falling here, but it's also about rain falling in the area", he said.
Journalists in the vicinity began to notice heightened activity overnight, with green netting and barricades being erected, and a number of ambulances arriving.
Journalists were told to leave the immediate area by 9am (3am BST). "No official word yet", he tweeted.
The boys, ages 11 to 16, and their coach became stranded when they went exploring in the cave after a practice game.
Flooding cut off their escape and prevented rescuers from finding them for nearly 10 days.
Thai Navy SEALs are working on the rescue mission, according to The Washington Post.
Around 1,000 people are involved in the complex rescue operation.
A multinational rescue operation led to their being found safe on a dry ledge, but their extraction through narrow, still-flooded accessways has posed a unsafe challenge, especially amid concern for their health after being trapped without light or nourishment for so long.
"Now and in the next three or four days, the conditions are flawless [for evacuation] in terms of the water, the weather and the boys' health", rescue-operation chief Narongsak Osottanakorn said Saturday.
Thai officials are stressing that they may have to act very soon - meaning within the next couple of days.
Sustained heavy rains could make the water rise to the shelf where the children are sitting, reducing the area to less than 108 square feet, he added, citing estimates from cave divers and experts.
Narongsak said the first boy was expected to be brought out of the cave by around 9:00 pm (1400 GMT) after navigating the planned six-hour journey.
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"We are ready. The boys are ready and strong enough to come out".
'If we did not carry out the mission today we might not have been able to get them out.
While the boys have been regaining their strength after rescuers took them high energy foods, and experts have been training them in diving techniques, for the unsafe and highly technical dives required to escape.
"Don't be anxious, I miss everyone".
Another wrote: "Nick loves Mum and Dad and siblings". Do take good care of yourself. "Aunty, can you please tell granny to prepare vegetable juice and pork snacks?" he wrote.
"I love you Dad, Mom".
Another joked: "Teacher, don't give us lots of homework!"
The football coach who took the boys into the cave apologised to parents, but they wrote he was not to blame.
"To the parents of all the kids, right now the kids are all fine".
He says the best-case scenario is to drain the water to a manageable level and float the kids out on dinghies. I love you,"another said".
The conditions of the boys and their coach will affect how and when they are extracted, Osatanakorn noted, saying they may not all be taken out at the same time. The 13 were having health evaluations and rehabilitation, and were being taught diving skills.
The team relied on drinking water that dripped from stalactite formations to survive, and have since been consuming high-protein liquid food after being found by rescuers. A major concern of the rescuers is that oxygen levels in their safe space could fall dangerously low.
"We hope that, in some way, our words of support may help bring them a little peace and courage in these hard moments of uncertainty and concern".
A former Thai navy SEAL passed out making the dive Friday and died.
Dr Harris, another Australian, a friend of his, and six Australian Federal Police divers are a key part of the rescue team.
Authorities continue to pursue a third option, which is finding a shaft or drilling into the mountain in which the cave is located to find a sort of back door entrance.
Billionaire entrepreneur Elon Musk tweeted that a team from his rocket company SpaceX in Los Angeles is building a mini-sub to help with the rescue.