The rescued boys are likely to stay in Chiang Rai hospital for 48 hours undergoing medical tests to check their health after they swam through dirty floodwaters to exit the cave.
Several ambulances and helicopters have been spotted near the site to safely transport the boys once rescues have been made.
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.
There are now five members of the Wild Boar football team now left in the cave.
Dozens of foreign divers and other experts from around the world were brought in to help the rescue effort, working alongside the Thai Navy SEALs.
The eight rescued boys were recuperating in a hospital from their ordeal huddled together on a tiny patch of higher ground where they had sought refuge after a rainstorm flooded the massive Tham Luan Nang Non cave complex as they were exploring it after soccer practice on June 23.
Prime Minister Prayuth Chan-ocha visited the cave to inspect the rescue operation, with navy rescuers giving him a rousing cheer.
The first four boys rescued from the cave are apparently now recovering well in hospital, demanding bowls of fried rice.
On Sunday, officials decided they could no longer wait, as conditions were "as flawless as they will be".
"You can't make a horror movie that would even compare", said Anmar Mirza with the National Cave Rescue Mission.
News of the release of the first four children on Sunday was greeted with elation in Thailand but rescuers say there are still significant risks with a majority of the boys still to undertake the risky 3.2km (2 mile) journey through the jagged, narrow and muddy cave.
Authorities have said the boys are being held close to divers and wear oxygen masks to enable normal breathing.
After the four boys were removed from the cave, heavy rain started falling. They are still quarantined away from their parents, who have been able to see them through a glass window but not touch or hug them.
The children's families have not been told which boys have been rescued. The delivery announcement comes on the second day of an operation to remove the boys. Four boys and their coach remained inside the cave.
Narongsak Osatanakorn, the head of the joint command centre coordinating the operation said: "The factors are as good as yesterday ..."
So far, rescues have been spaced out to allow for the divers to rest and the oxygen tank to be restocked. Highlighting the extreme dangers, a former Thai Navy SEAL died Friday while replenishing the oxygen canisters laid along the route.
But although the eight were rescued, there were concerns they may have contracted an illness while in the cave.
The world has been hooked on the fate of the group of Thai boys trapped in a cave and the heroic attempts to rescue them.
Police and military personnel shield the fifth survivor with umbrellas as he is transported on a stretcher at a military airport in Chiang Rai, Thailand, on Monday.