Engineers have been pumping water out of the cave for a week and a temporary respite from the rains has lowered water levels.
More than 1,000 Thai military personnel are at the site, as well as teams from seven countries including the UK, US and Australia. Kamolroj Ekwattanakij, a communication officer with the Thai Navy Seal, told CNN that divers also brought the weakened boys food, mainly grilled pork, sticky rice and milk.
His team is considering rescue options, but would not attempt to have them dive out without doing more checks and a dummy run. "We will continue to support the Thai Navy SEALS in the best way we can".
A team of Thai Navy SEAL divers - including a medic - have joined them on the bank, while rescuers pour over evacuation plans from the Tham Luang cave complex in northern Thailand before heavy rains return and raise the water level.
Interior Minister Anupong Paojinda said the 13 footballers would be brought out of the cave through the passage leading to its main entrance.
While the aim is to take the boys out of the cave, that depends on the ability of the rescuers to pump water out of the cave and also the health of the children and coach.
Thai authorities said they are committed to "100 percent safety" when they consider how to extract the youth soccer team from the partially flooded cave.
A Thai provincial governor says the 13 people who had been missing for more than a week have all had an "informal" medical evaluation inside the cave and most are in stable condition and none are in critical condition.
It was particularly hard for the rescuers to locate them because the cave system consists of dark, narrow bends that sometimes fit only one person, Ben Reymenants, one of the divers involved in the search, told Sky News. The thirteen people appeared to have been stranded in the dark tunnels by a sudden and continuous downpour after they entered the cave.
The search for the group had gripped the nation as it was unclear where they were or whether they were even still alive.
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Despite the peril ahead, families and friends, some of whom have maintained a constant vigil outside the cave, hugged each other and cheered at the news.
Thailand's prime minister Prayuth Chan-ocha has thanked the global experts who assisted in the search.
One Thai twitter user said that he was "crying in (a) taxi" at the news.
Aged between 11 and 16, the boys went missing with the 25-year-old coach after soccer practice on June 23 after they set out to explore the Tham Luang cave complex in a forest park near Thailand's northern border with Myanmar. The elevated rock where the boys and their coach were found is about 4 km (2.5 mi) from the mouth of the cave.
Pattaya Beach, the section of the cave where the boys are sheltering on a mud bank, is 5km into the 10km cave network and the conditions of the dive are treacherous, with nearly no visibility and rushing waters.
His Majesty the King has endorsed an order transferring Mr Narongsak to serve as the governor of the smaller province of Phayao, assistant government spokeswoman Col Taksada Sangkachantra said.
Divers had to navigate a series of sharp, narrow bends in near-darkness.
Narongsak explained early Monday that fixing rope lines and deploying oxygen tanks along their route will allow the divers to operate. None of them know how to swim, Dr Thongchai said. That could take as long as months, however, given that Thailand's rainy season typically lasts through October. "There is current. The visibility can be zero at times".
The eyes of the world are focused on the dramatic discovery of 12 young soccer players and their coach alive but still trapped in a remote flooded cave - more than a week after they disappeared - and desperate efforts are underway to feed them and try to find a way to get them out.