Still four more teenagers and their coaches are trapped inside the cave. The rescuers planned to bring them out on Tuesday.
Thai Navy confirmed the rescue of four more boys on their Facebook page on Monday.
The teenage football team was trapped 16 days ago after entering the cave of Chiang Rai in northern province.
On Sunday, teenagers started pulling out of the cave. After four out of the day, the operation was postponed to make fresh preparations.
Divers started rescue operation again at 11 am (04:00 GMT) local time on Monday.
On Sunday, the number of divers was increased for rescue work compared to Sunday. Although 13 foreigners and five Thai divers are doing the main task to bring out the teenagers from the cave, the BBC said.
Meanwhile, there was heavy rains in Chiang Rai province on Sunday night. Because of this, there was concern about the kidneys and their coaches inside the cave. However, due to rain there was no change in water level in the cave, Thai authorities said. Rather than on Sunday, the situation inside the cave was favorable on Monday, Rescue workers said.
The 12-member teenage football team and their 25-year-old coach entered the 'pillar lounge' cave in Chiang Rai province of North to celebrate the birth anniversary of a teenage boy after regular training on 23 June.
The team was trapped due to the heavy rain pouring water into the cave inside the cave.
Two British divers were found in the group 10 days after the disappearance. They are between 11 and 16 years of age.
The divers started pulling out teenagers from Sunday. It is possible to get four teenagers out on that day. The operation was postponed due to the night and preparations for the divers to enter the cave again.
Four teenagers brought out on Sunday are said to be healthy. After being rescued from the cave, Chiang Rai was taken to the hospital in the helicopter. Due to weakness of the body for a few days of starvation, they have been separated so that they do not get infected with any infection.
Rescuers have been taken to the same hospital on Monday. Researchers say they have some problems with cold, but their physical condition is good.
The names of the boys who have not been released till now have been published. It has been done to honor the feelings of the families of the children, officials said. Although the family was still not allowed to meet them.
50 foreigners and 40 divers from Thailand Navy are directly participating in a full-fledged campaign to bring the children out of the cave.
They have to fight against time. Because the monsoon season has started in the country and it has been forecasting heavy rain in the next few days. There may even be a storm in even weeks.
On Saturday night, after a forecasts from the Department of Meteorology, a physician from Australia advised the teenager to check the health of the boys and start the drive to bring the group out.
The final campaign started to bring the boys out of the morning the next day. Described as "de-day", Narcissi Ososammon, Chief of the rescue operation