The message of hope came a day after the death of a Thai rescue diver, a grim turn in what began two weeks ago as a celebration of one of the boys` birthdays at the Tham Luang cave complex in the northern province of Chiang Rai.
A team of Thai Navy SEALS, soldiers, police and volunteers has been working frantically to drain the cave since the group was discovered on Monday, Reuters reported.
They are now teaching the children, aged between 11 and 16 and not all of whom are strong swimmers, to attempt a treacherous dive through narrow, submerged tunnels.
"The next three to four days from now is the best and most ideal time for the rescue operation," Narongsak Osottanakorn, the rescue mission chief and former provincial governor, told reporters.
"The current situation, with the air and water levels and the boys` health, is the best yet," he added.
"We`re still at war with water and time. The discovery...was just a small victory, but that doesnt mean the war is over until we have won all three battles: discovery, rescue, and return home."
In another development on Saturday, authorities confirmed the boys had communicated by letter with their relatives, many camped outside the cave`s entrance, for the first time since they were found.
An attempt to pass a phone to the boys earlier in the week failed.
In one letter, the boys list the foods they want to eat once safely home, such as fried chicken and "hot pan barbecue" and beg their teachers not to assign too much homework.
The coach, Ekapol Chanthawong, told parents in a separate letter that he would "take the very best care" of the boys and apologised for putting them through their ordeal.