SEAL commander rear admiral Arpakorn Yookongkaew said seven members of his unit - including a doctor and a nurse - are now with the group.
Rescuers are racing to pump water from the Tham Luang Nang Non Cave before the predicted arrival of heavy rain, which would complicate efforts to free the team, who have been trapped 1km underground for the last 10 days.
The young footballers went into the cave as part of an initiation, one of the divers who helped locate them has said.
The boys reportedly went into the Luang Nang Non Cave in order to write their names on the walls.
They were "wading in and trying to go to the end of the tunnel, sort of like an initiation for local young boys to… write your name on the wall and make it back," Ben Reymenants told Sky News.
Thai interior minister Anupong Paochinda has said the boys will be brought out the same complicated route the rescue diverse took to find them.
He said efforts to pump out the water would continue, but that it was clear there were areas which could not be drained.
The children might need diving gear, he added, and would be accompanied by two divers each on their way out, according to the Bangkok Post.
''Diving is not easy. For people who have never done it, it will be difficult, unlike diving in a swimming pool, because the cave's features have small channels,'' he said. ''If something happens midway, it could be life-threatening.''
The Thai government has released advice on the rehabilitation of the football team if and when they get out.
It says survivors and family members may experience post traumatic stress disorder (PTSD). Once out, they should be provided with a "calm and peaceful environment" to create "a feeling of safety and stability".
"Families should also consult with a psychiatrist should the children exhibit symptoms of PTSD, so that they can receive the necessary therapy or medication, and be available and attentive if the child wishes to discuss their feelings or experiences," it adds. "Families should also encourage their children to engage in stress-free activities and avoid leaving the children alone."
Ben Reymenants, who was around 400m behind the British team who found the boys, told Sky News authorities have limited options going forward. One would be to teach the children to scuba dive, another would be attempting to pump the water out of the cave.
Local media say the boys have been brought food and mineral salts by diving experts to rebuild their strength. The group survived on next to no food or fresh water.
The US ambassador to Thailand has expressed satisfaction with the first stage of the rescue.
A US military team of about 30 specialists flew in from overseas to assist in the rescue mission.
Ambassador Glyn Davies said: "The American people join Thais in celebrating the discovery of the football team and their coach in Tham Luang cave. We will continue to support Thai authorities in their efforts to safely bring home the players and their coach."
Despite a warning of "months", it now appears Thai authorities are going to attempt to extract the children ahead of fresh rains expected later this week.
“As rain is forecast in the next few days, the evacuation must speed up. Diving gear will be used. If the water rises, the task will be difficult. We must bring the kids out before then,” Anupong Paojinda, the interior minister, said according to the Bangkok Post.
“Diving is not easy. Those who have never done it will find it difficult, because there are narrow passages in the cave. They must be able to use diving gear. If the gear is lost at any moment, it can be dangerous to life.”
Hello and welcome to The Independent's live coverage as Thai authorities, supported by an international team of experts, attempt to rescue a dozen boys and a football coach trapped in a cave for the last 10 days.
Mr Yookongkaew told a news conference his team members "have given the boys food, starting from easily digested and high-powered food with enough minerals".
He said that having the boys dive out of the cave was one of several options being considered. If it were employed, he said they "have to be certain that it will work and have to have a drill to make that it's 100 percent safe".
In video shot by British divers as the group were found, torchlight reveals boys in shorts and red and blue shirts in an underground cavern beside an expanse of water.
With the onset of the rainy season, Thai navy captain Anand Surawan had initially warned the group could be trapped for months.
"[We will] prepare to send additional food to be sustained for at least four months and train all 13 to dive while continuing to drain the water,” he said.
Police have said the 25-year-old football coach who led the team into the cave network could face legal action.
An international team of divers, including from Britain, struggled through narrow passages and murky waters to find the boys, aged between 11-16, and their coach late on Monday night on an elevated rock about 2.5 miles from the mouth of the cave.
"How many of you are there - 13? Brilliant," a member of the multinational rescue team, speaking in English, tells the boys. "You have been here 10 days. You are very strong."
News of the boys' survival sparked jubilation in a nation that has been gripped by the harrowing drama.
"Thank you," one of the boys says.
One boy asks when they will get out, to which the rescuer answers: "Not today. You have to dive."
The boys were found in weak condition, but with only minor injuries.
Interior minister Anupong Paochinda said rescuers needed to intensify efforts to reduce water levels in the cave.
Rain continued to fall in Chiang Rai on Tuesday and was forecast to intensify from Wednesday.
Additional reporting by Reuters.
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