The four boys will join four others rescued Sunday out of a group of 12 and their soccer coach.
"Today (Tuesday) we hope to be faster", Narongsak added, of the complex and risky operation that involves diving through narrow, flooded chambers.
He said a medic and three Seals in the cave, who have been looking after those trapped, will also come out.
Rescuers in Thailand are racing against predicted monsoon rains - that could kick up in the middle of this week - to free the remaining boys still trapped in a flooded cave.
Jedsada Chokdumrongsuk, permanent secretary at the Public Health Ministry, said the boys rescued Sunday were able to eat normal food by Tuesday, though they couldn't yet take the spicy dishes favored by many Thais.
Officials said all eight of the boys rescued so far were "good physically and mentally", though two of the four brought out on Monday had swollen lungs.
"The kids are footballers, are strong and have high immunity", Jesada said when asked why they survived so long.
Efforts were again suspended for the day Monday after the second set of four boys were extracted.
Family members have seen at least some of the boys from behind a glass isolation barrier, and Jesada said doctors may let the boys walk around their beds on Tuesday.
Four boys and their soccer coach remain in the cave.
Heavy rains lashed the northern Thai region late Monday and a steady downpour has continued Tuesday.
"It is certainly a risk and can take some time to manifest itself and make its presence known", said Andrew Watson, a specialist on rescues from mines and floods trapped. They also anxious about dwindling oxygen levels in the cave. They are assisting in transporting the evacuees through the final chambers of the cave system, and are providing medical personnel and other technical assistance to the rescue efforts, he added.
"All four boys have arrived at hospital, all are safe", Narongsak Osottanakorn, head of the rescue mission, told reporters of those rescued on Monday. Elon Musk recently pledged his team's help in rescuing the group. It is now unclear whether Musk or his technology will be used in the rescue efforts, but Musk confirmed via tweet that the submarine is in Thailand and ready to be used if needed.
In another post early Tuesday, this time on Instagram, several people were seen wading through the waters of the cave with headlights guided by rope.
July 9, American engineer and founder of SpaceX Elon Musk showed photos and videos of metal capsules created to rescue children from a flooded cave in Thailand.