The boys who were rescued on Sunday were strong and safe but needed to undergo detailed medical checks, he said. Workers have been labouring around the clock to pump water out of the cave, and authorities said Monday that heavy downpours overnight did not raise water levels inside.
"The mission has resumed", a government official closely involved in the mission told Reuters, declining to be identified.
The "Wild Boars" football team and their coach got trapped on June 23 when they set out to explore the vast cave complex after football practice and the tunnels became flooded.
Each boy is being accompanied by two divers through the dark and complex cave system.
Paojinda said officials met Monday morning to discuss the next stage of the operation and how to extract the remaining nine people from the flooded cave.
The unsafe bid to rescue the boys - aged between 11 and 16 - got going again hours earlier on Monday after a break to replenish oxygen supplies and make other preparations deep inside the cave complex in northern Thailand's Chiang Rai province. On Sunday four members of the "Wild Boar" team were successfully brought out from the cave, after authorities decided they had to rush ahead with a rescue operation to beat monsoon rains.
The Australian foreign minister, Julie Bishop, said in a TV interview on Monday morning she believed the boys would be brought out in groups of four.
The first four boys, from the group of 13, including the coach, were rescued on Sunday.
The first four boys to be rescued were led out of the cave by an global team of rescue divers on Sunday.
That brings to three the number of ambulances that have left the site Monday during the second day of a high-risk operation to bring the boys out of a labyrinth cave system made up of tight passageways and flooded chambers.
Narongsak said Monday's rescues involving 18 divers and a support team of 100 had taken nine hours, two fewer than the rescues on Sunday.
Thai premier Prayut Chan-O-Cha was also due to visit the rescue operation late on Monday.
Interior Minister Anupong Paochinda told reporters the rescued boys were in good health in hospital but did not give details.
There was no immediate word on their conditions.
Officials have yet to confirm the identities of the four boys freed. They wore full-faced masks "while hanging on to the bodies of rescue divers", Channel News Asia reported.
All those rescued from the Luang Khun Nam Nang Non cave are to be flown or transported by ambulance to the Chiang Rai Prachanukroh Hospital.
Medical teams previously said concerns included hypothermia and an airborne lung infection known as "cave disease", which is caused by bat and bird droppings.
"We expect that if there is no unusual condition. the 4 boys, 1 coach, the doctor, and 3 SEALs who have been with the boys since the first day will will come out today", he told a press conference to loud cheering.
"I'm hoping for good news", he said. Soldiers, medics, engineers and volunteers in yellow shirts milled around but the mood was relaxed. "I can help him with his homework", he said.
Relatives said the boys had been inside the labyrinthine complex during the dry season.
Hundreds of spectators and journalists have gathered in the area around the cave, hoping for news that the boys and their coach would emerge safely.