The head of the operation, Narongsak Osottanakorn, said a final operation would be "more challenging" because one more survivor would be brought out than the previous two operations, along with three Navy SEALs who have been accompanying them.
"Coordination and interaction with Thai military, Thai government, and other multinational civilians and government entities remains extremely positive and effective", he said.
The rescue missions take almost half a day to complete.
Asked whether the remaining four "Wild Boars" team and their coach would come out at the same time in the next rescue effort, he said: "It depends on the plan".
The leaders overseeing the desperate and unsafe rescue of 12 young soccer players and their coach from a flooded cave labyrinth in northern Thailand were only half joking when they quipped that success was in the hands of the rain god Phra Pirun. As of this midday Monday, eight of the 12 boys had been rescued, and operations were ongoing. Last week, a former Thai navy diver died while preparing for the operation.
The saga has dominated global headlines, with the team spending nine days unaccounted for inside the cave, before British divers found them - emaciated and dishevelled - huddling on a muddy bank above the flooding. "His sacrifice will not be forgotten". They'll also be bringing back 3 Navy SEALS and a medic who have been in the cave with the team since the first day of the rescue efforts.
"But when I saw that he was alive and breathing, it felt very good".
Somboon Sompiangjai, 38, the father of one of the trapped boys, said parents were told by rescuers ahead of Sunday's operation the "strongest children" would be brought out first.
As we enter the day three of the Thai cave rescue mission, the public health permanent secretary Dr Jesada Chokedamrongsuk, from the Ministry of Public Health and Chiangrai Prachanukroh Hospital, spoke to the media this morning (local time) about the health of the eight boys who have been rescued so far.
Thai Prime Minister Prayuth Chan-ocha, speaking Tuesday before the final rescue was completed, said the boys were given an anti-anxiety medication to help with their perilous removal from the cave.
He said they would need to keep at least two metres away for their boys for at least 48 hours, until "we are sure there is no infection, then they can visit them normally".
"Everyone is in high spirits and are happy to get out".
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 Tuesday.
A message posted on the English Premier League club's Twitter account said: "Our thoughts and prayers are with those affected".
The submarine is named "Wild Boar" after the name of the football team.
The boys are being monitored in the hospital for illnesses and other health issues from being stuck in the cave for two weeks.