It comes a day after the head of the rescue mission said conditions were "perfect" for the evacuation to begin, and amid fears that incoming monsoon rains could soon thwart the plan.
Interior Minister Anupong Paojinda had said early Monday that the same group of expert divers who took part in Sunday's rescue would return to extricate the others because they know the cave conditions and what to do.
The team is trapped more than four kilometres from the mouth of a cave, and a series of obstacles - including low-visibility water, extremely narrow passages and the boys' inability to swim - stand between them and freedom.
The boys and their coach had been stranded in Tham Luang Nang Non when they went exploring in the cave after a scrimmage. Monsoon flooding cut off their escape and prevented rescuers from finding them for nearly 10 days.
However, efforts to extract the remaining boys who are trapped in a flooded Thai cave have been paused for at least 10 hours, the operation commander told reporters after six were rescued.
It was unclear who was inside the ambulances or the helicopter.
Boring Company CEO Elon Musk is now part of an worldwide team of engineers, divers, and other experts working to rescue a group of boys from a Tham Luang Nang Non cave in Thailand. General Kongcheep Tantrawanit said, referring to the area where rescue workers had set up a base. The rescuers and boys will have to contend with navigating tight passageways filled with muddy water and strong currents, as well as with oxygen-depleted air.More news: Princess Charlotte, Prince George's hilarious expressions captured during RAF flypast
More news: Norwich facing competition from multiple Championship clubs for Wilson loan
More news: A look at what’s ahead in the World Cup
The cave rescue mission went faster than practice drills over the last few days, according to Osotthanakorn.
Four of the boys were rescued on Sunday, and authorities said the next phase could begin any time within a 10-hour window that began about 7 a.m. Monday. We will have to do the next mission as successfully as the one we did today.
Rescue chief Narongsak Osottanakorn told journalists near the Tham Luang cave site: "Today is the D-day".
The rescue of the first four boys had brought joy and relief to the families and friends of the 13, with one school friend of some of the boys telling media that he is very happy and thanking the rescue team for bringing his friends out. Two others were brought out about two hours later.
Guerrero says she's glad rescue operations to save the group of boys and their coach trapped in a Thai cave are moving swiftly before water levels in the cave rose even higher.
"On behalf of the United States, congratulations to the Thai Navy SEALs and all on the successful rescue of the 12 boys and their coach from the treacherous cave in Thailand", Trump said on Twitter. An Australian doctor with cave diving experience examined the boys on Sunday and declared them fit for the operation.
Mild weather and a break in the rain had lowered the water to the lowest levels since the boys were found.
Narongsak said the operation was going "better than expected". It was raining Sunday, but Narongsak was optimistic that the rescue could continue Monday.