The entire operation to get all 12 boys and their football coach out of the cave could take two to four days, depending on weather and water conditions, said Thai army Major General Chalongchai Chaiyakam.
The daring and risky bid to rescue the boys - aged between 11 and 16 - was suspended by the mission chief late on Sunday to replenish oxygen supplies and make new preparations, which he said would take at least 10 hours.
He said that four boys were rescued in Sunday's effort.
Narongsak said he didn't know when the team would be able to rescue the rest of the boys but he estimated at least 10 hours and no more than 20. The latter option is extremely risky, and the arduous trip caused the death of a former Thai Navy SEAL as he lost consciousness underwater while placing extra air tanks inside the cave to allow other rescuers to reach the group.
The story of the "Wild Boars" soccer team, who first ventured into the caves more than two weeks ago before flood waters trapped them inside, has gripped Thai and global media.
In total, the mission could last several days, he also said, though the team of worldwide divers on the site are apparently feeling "buoyed" by the success of the operation so far.
The names of the rescued boys have not been released out of "respect for those families whose sons are still trapped inside", the mission chief said.
"Imagine marathon runners. It's like when they reach the finish line exhausted", said the source. A family member told CNN Monday that they hadn't been told which boys had been pulled out, and who is still trapped in the cave.
The 12 boys - members of a Thai youth soccer team and aged between 11 and 16 - and their coach were trapped in the Tham Luang Nang Non cave system June 23 following heavy rains; however, they were found alive a week later by divers.
Four boys were extracted on Monday, the Royal Thai Navy has confirmed.
They were taken to Chiangrai Prachanukroh Hospital where their four teammates rescued on Sunday had been tested and waiting for an all-clear. On Sunday, four boys were safely evacuated from the cave.
Ten rescuers put on scuba gear and headed into the Tham Luang cave network around 11 a.m. local time on Monday to extract the remaining members of the junior soccer team and their coach, Thai officials said. It rained overnight as well. On Friday, a former navy SEAL who suited up again to volunteer died on a dive to resupply the oxygen needed for the long and arduous dive.
Authorities have repeatedly said the rain could re-flood crucial parts of the cave complex that have been drained and make the escape route much harder or even impossible to navigate. They say rescuing the eight remaining boys and their soccer coach could take up to four days. The soccer team is trapped in a complex cave system filled with tight underwater passageways.