Pad kra pao, a Thai chicken dish, was said to be the first meal that the four boys asked for.
Thirteen foreign divers and five members of Thailand's elite navy SEAL unit make up the main team guiding the boys to safety.
Authorities have said extracting the entire team from the cave could take up to four days, but two straight days of success raised hopes that it could be done faster.
An Australian doctor was involved in the operation.
Officials will have to spend about 20 hours preparing all the necessary support equipment, said the former governor, adding that he was confident the rescue team would be able to operate with greater ease and to shorten the time spent by between 4-5 hours.
The boys are said to be generally in good health but doctors are still evaluating whether they could have picked up any unsafe infections, such as the potentially lethal leptospirosis, while inside the damp cave for two weeks.
Interior Minister Anupong Paochinda also said the boys were in good health.
Authorities have not confirmed the identity of the rescued boys. They say rescuing the eight remaining boys and their soccer coach could take up to four days. Some of the parents told Reuters they had not been told who had been rescued and that they were not allowed to visit the hospital.
School students in Ahmedabad play for the well-being of 12 soccer players and their coach who were trapped in a cave in northern Thailand. "The boys' strength, the plan - today we are ready like before".
"The rescue has been enormous", said volunteer helper Somjit Saenset, 56. He said the "tiny, kid-size submarine" was designed using "the liquid oxygen transfer tube of [SpaceX's] Falcon rocket as hull".
The boys who were rescued on Sunday were strong and safe but needed to undergo detailed medical checks, he said.
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"Our job is not completely done. The rest of the kids are in the same spot".
Heavy monsoon rains lashed the mountainous Chiang Rai region, where the Tham Luang Nang Non cave is situated, for several hours overnight on Sunday. "Their plan is designed for rescuing four".
"We are anxious every day", she said.
Rescuers took advantage of a break in the rain on Sunday to launch the mission earlier than some expected. They were accompanied by two professional divers each throughout. Light enough to be carried by 2 divers, small enough to get through narrow gaps.
The boys and their coach became trapped on June 23 when they went exploring in the cave after a soccer game. The diver, the first fatality of the rescue effort, was working in a volunteer capacity and died on a mission to place air canisters along the passage to where the boys are, necessary for divers to safely travel the five- to six-hour route.
Dr Richard Harris, an anaesthetist from Adelaide, went into the cave at the specific request of Thai authorities.
People around the world are following the developments in Thailand.
But then oxygen started running low in the cave, and officials also anxious the little piece of real estate the boys and their coach have could be lost.
Authorities have said the boys are being held close to divers and wear oxygen masks to enable normal breathing.
At the hospital in Chiang Rai, green canvas sheets had been put up to block the entrance from view. The rescue team is the same team with a few replacements. That's how deadly the rescue mission is! .
"For the people who are now bringing the 13.out of the Tham Luang cave, he (Prayuth) wishes safety and success", government spokesman Sansern Kaewkamnerd said.