Four boys were brought out of the cave Monday and are "safe and conscious", Chiang Rai province acting Gov. Narongsak Osatanakorn said.
A Reuters witness near the Tham Luang cave in the northern province of Chiang Rai saw medical personnel carrying two people out of the cave to waiting ambulances on Monday evening.
Four boys and their coach remain in the cave Monday, CNN reports.
But rescuing the remaining five people, which includes the boys' 25-year-old soccer coach, could take more than one operation, Narongsak said.
The operation began at around 11 a.m. local time on Monday and is expected to finish for the day around 9 p.m, reported the BBC. It was unclear who was inside the ambulance or the helicopter.
Rescue mission chief Narongsak Osotanakorn said Monday's rescue operation was two hours shorter than the previous one after authorities reviewed the process to make it sharper.
On Sunday, officials waited until several hours after the rescued boys had been transported to hospitals to announce their rescue.
The billionaire entrepreneur has been tweeting proposals and offering his services to the Thai government in its efforts to extract the 12 boys and their soccer coach from a partially flooded cave.
Four boys were successfully rescued from the Tham Laung cave area on Sunday in a delicate and lengthy operation.
Those still inside the cave are perched on a small muddy ledge 4 kilometers (2.5 miles) from the entrance, surrounded by floodwater and with a limited supply of oxygen.
Two divers have been escorting each child, following a cave line that stretches a mile and a half. It takes the divers about eight hours to get into the cave, reach the boys, and bring them back out.
A total of eight boys were removed from the cave on Sunday and Monday.
On Monday, skies were largely clear over the site but rain has been forecast for at least the next three days.
They are then taken to hospital in Chiang Rai.
"The children complained that they were hungry and wanted holy basil stir-fried rice". Still, they were undergoing medical checks in a hospital and were not yet allowed close contact with relatives due to fear of infections, who were able to see them through a glass partition.
Authorities had said that incoming monsoon rains that could send water levels in the cave rising, coupled with falling oxygen levels in the enclosed space, added to the urgency of getting those trapped out. Visitors would need to wear sanitized clothes and stay two meters away from the children.
Officials lavished praise on the Thai and global divers who executed the unsafe rescue mission, guiding boys who can barely swim and have no diving experience through a treacherous 4-kilometre-long (2 1/2-mile) escape route that twisted and turned and rose and fell inside the mountain cave complex. The Thai authorities have been pumping out water from the cave system ever since locating the missing soccer team, but that wasn't enough to remove all the water.
It took hours to place oxygen tanks and guide ropes along the narrow tunnel leading to the boys.