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.
Rescue mission chief Narongsak Osottanakorn said it had resumed, with divers re-entering the cave at 11am local time (4pm NZT).
The boys have been trapped in the Tham Luang Nang Non cave since June 23 when they and their coach entered and were then cut off by flash flooding.
The Seals posted a count on their Facebook page, concluding with "Two days, eight boars", a reference to the name of the boys' football team.
Chiang Rai acting Gov. Narongsak Osatanakorn, who is heading the rescue, had said the second phase began at 11 a.M. Monday and authorities "hope to hear good news in the next few hours". Four came out Monday, and it is possible Tuesday's plan was to bring out four more. He said recent rains had not affected water levels in the cave and conditions were expected to be "as good as they were on Sunday", reported The Guardian.
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.
Eight boys have now been extracted.
Thai premier Prayut Chan-O-Cha was also due to visit the rescue operation late on Monday.
The boys are all healthy and safe, according to multiple reports.
There was no word on the condition of any of the people brought out on Monday.
One of the biggest concerns in the rescue operation is an area of the cave that is just 15 inches across so the boys have to separate from the divers in order to fit through.
The four boys rescued Sunday are recovering in a nearby hospital and are yet to see their parents.
"This morning they said they are hungry, and they wanted phad kra pao", he said.
'We have not been told which child has been brought out. The stretcher was loaded into the back of the ambulance as medics rushed in the side door.
"I feel very happy, everybody is happy", said Hnin Jaiwong, the mother of one of the trapped boys, 13-year-old Sompong Jaiwong.
"I don't know if he is out, they didn't tell us", she said as she rested in a hut close to the mouth of the cave.
The cave complex is off-limits during the rainy season, which usually runs from May to October when downpours can quickly flood it.
The fate of the boys and their coach has gripped Thailand and drawn global media attention.
The president of football's governing body, FIFA, has invited the boys to the World Cup final in Moscow on Sunday if they make it out in time.