The children, who are aged between 11 and 16, had become trapped in the Tham Luang caves in Chiang Rai after heavy rain triggered a flash flood that prevented them escaping through a narrow tunnel.
Chiang Rai's Governor Osatanakorn said the divers had concentrated on securing a rope line and placing oxygen tanks along the narrow passageway that they think will lead them to the boys.
"We won't bring them out until we find a totally safe way", said Mr Narongsak, who is officially in charge of operations at the cave. "I haven't had anything to eat".
The condition of the group was not immediately clear after days underground.
Mr Narongsak said the divers located them about 300-400 metres past a section of the cave that was on higher ground and was thought to be where the team members and their coach may have taken shelter.
Sura Jeetwatee, a doctor who is part of the operations, said the boys were able to walk and had survived by staying where they were and drinking water that dripped from stalactite formations.
Aisha Wiboonrungrueng, a mother of one of the missing, 11-year-old Chanin Wiboonrungrueng, smiled and hugged her family.
"Today we will re-enter the second chamber that we found and try to find passages that could lead to other chambers", Wirachai said.
The council said many of caves have been explored by British cavers and divers, "bringing with them valuable knowledge of the layout of overseas cave systems".
"They should be okay without food for eight days", said Dr Somsak Akkasilp, the director-general of the Medical Services Department.
On the footage released on the Thai NavySEAL Facebook page, the boys can be heard yelling, "thank you", as the rescuer asks, "how many of you?", to which on of the groups answers, "13".
"So we will run two operations, opening this channel to get through and maintaining so all the rescue team can get inside and work there".
Interior Minister Anupong Paojinda said Tuesday that the boys may need to swim out using diving equipment ahead of bad weather forecast for later in the week.
The divers have been stymied again and again by muddy water rising to the ceiling of the chamber, forcing them to withdraw for safety reasons.
With water levels dropping, they resumed dives Saturday, re-entering a chamber from which they had retreated earlier in the week.
Prime Minister Prayuth Chan-ocha thanked the global experts and rescuers who helped locate the missing for their "tremendous efforts".
It took them several hours to reach the group on Monday.
Thailand has been a nation transfixed by the plight of the "Wild Boar" team, with social media lighting up in support of the group and the country's deeply spiritual reflexes stirred into action.
But one cave rescue expert was cautious about this approach. An official Australian group has followed a US military team, British cave experts, Chinese lifesaving responders and several other volunteer groups from various countries.