The aide, Sitthichai Klangpattana, didn't comment on the boys' health or say how well the operation has gone.
The 12 boys - ages 11 to 16 - entered the massive cave complex on the frontier of Thailand and Myanmar with their 25-year-old coach on June 23.
The Thai youth soccer team and their coach became trapped in the cave they were exploring on June 23 after heavy rains flooded exits.
Rescue mission chief Narongsak on Monday said the operation on the second day started at 11am.
A medic and three Thai Navy SEALs who have stayed with the boys on a small, dry shelf deep in the flooded cave will also come out, he said.
A helicopter with the boy on board was seen taking off shortly afterwards to the cheers of the crowd below.
"The water level is not worrisome", he said, the paper reported.
How long will the rescue operation take?
Soldiers arrive outside the Tham Luang cave complex in the northern province of Chiang Rai, Thailand, July 8, 2018. He said it was out of respect for the families whose sons were still trapped in the cave.
'Better than expected' rescue suspended for night; four out
Reuters news agency reported that six boys have been rescued, citing a senior member of the medical team involved in the rescue. The boys, aged between 11 and 16, and their 25-year-old coach belong to a local team called Moo Pa ( Wild Boars ) Academy.
Sunday night, teams of divers brought out four of the trapped boys to waiting ambulances.
The operation is set to resume on Tuesday to evacuate the remaining five.
The eight freed boys of the Thai soccer team may have seen daylight for the first time in weeks, but they still can not come face-to-face with their loved ones.
Thai Prime Minister Prayut Chan-o-cha paid a visit to all the rescue teams on Monday before leaving to see the evacuees at the hospital in the city centre.
It was not clear who was inside the ambulance or the helicopter.
It is understood the same divers who rescued the first four boys have been given the job of getting the remaining team members out.
Narongsak said that experts told him new rain could shrink the unflooded space where the boys are sheltering to just 10 square meters (108 square feet). Previously, round trips through the cave network would take about 11 hours.
The fate of the boys and their coach has gripped Thailand and drawn worldwide media attention.
The search and rescue operation has riveted people both in Thailand and internationally, with journalists from across the globe traveling to this town along the border with Myanmar to report on the ordeal.
But speaking in Bangkok, Interior Minister Anupong Paojinda said the four pulled from the cave "are strong and safe" and in the care of doctors.
Trump's crackdown on immigration threatens Canadian lobster harvesters
US officials told CBC News the agents were there to "enforce immigration laws and other violations of federal law". In a statement, the Association believes this was part of a regular exercise conducted by officials.
Five more boys, including the coach, are still trapped in the Tham Luang cave.
There was no word on the condition of any of the people brought out on Monday. Crews should replenish air tanks along the route before rescuing the others.
Monday's rescue effort took about nine hours, two fewer than the day before, in a sign of growing confidence and expertise.
However, Saturday night, Musk tweeted that the cave was now closed for the rescue by divers, adding, "Will continue testing in LA in case needed later or somewhere else in the future".
Meanwhile, Thailand's weather department said there was a 60 percent chance of rain on Monday with thunderstorms forecast throughout the week.
Even tech billionaire Elon Musk has been lending a helping hand. If the tests were successful, the sub was to be placed on a 17-hour flight to Thailand.
A witness near the cave told the Reuters news agency that medical workers carried four people to emergency rescue vehicles. Two divers were assigned to each child to help them navigate the unsafe, narrow passageways.
A device by Elon Musk's SpaceX and The Boring Company, created to help rescue the remaining members of a soccer team trapped in a flooded cave in Chiang Rai, Thailand, is being tested in a swimming pool in Los Angeles, California, in this still image taken from an undated video obtained from social media.
"According to divers who have made the journey, this is capable of maneuvering through all passages", Musk wrote on Twitter. They are then taken to hospital in Chiang Rai. They have not been reunited with their families yet due to infection concerns.
TROPICS: 2 systems may form this week in Atlantic
The NHC said that the system is expected to dissipate however it will still bring gusty winds and showers to the Lesser Antilles. On Thursday afternoon, Tropical Storm Beryl was 1,330 miles east-southeast of the Lesser Antilles moving west at 16 mph.