The Facebook page of the Thai Navy Seals, who have been central to the rescue operation, was updated on Monday night to say "two days, eight boars" - a reference to the Wild Boars, the name of the boys' football team.
A second mission, which rescued another four boys, commenced on Monday, July 9.
In the past two days, eight boys were rescued and are now in a hospital isolation ward while they are tested for any possible infections.
On Sunday, teams of divers brought out four of the trapped boys but waited several hours before confirming their safe rescue.
Harris' colleagues and fellow rescuers lauded his commitment to the mission and how vital his expertise was in bringing the boys out to safety.
The "Wild Boars" soccer team and their coach got trapped on June 23 while exploring the cave complex in the northern province of Chiang Rai after soccer practice and a rainy season downpour flooded the tunnels.
The boys underwent x-rays and blood tests and two who had signs of pneumonia were given antibiotics and are in a "normal state", he said, adding they will all remain under observation in hospital for a week.
The boys' ordeal has transfixed millions of people, as a massive rescue effort was planned and mounted. It is believed the youngest child, aged 11, was one of the last to be freed, although it was the boys' 25-year-old coach who was the last to be rescued.
On Sunday, expert divers brought out the first four of the 13 who were stranded in the huge and waterlogged Tham Luang complex.
Rescue organizers said they need 20 hours to replan and replenish oxygen supplies, with the next rescue mission expected to come some time on Tuesday afternoon, weather permitting. Doctors were being cautious because of the infection risk and were isolating the boys in the hospital.
Underscoring the danger behind the mission, Ivan Karadzic said, "They are diving in something considered an extremely hazardous environment". We've started giving them "medical food" this morning.
Rescuers are moving ahead quickly because they are afraid monsoon rains will completely flood the caves.
He wrote in a tweet posted this morning: "Mini-sub is ready if needed".
Soccer's governing body, FIFA, has invited the boys to the World Cup final in Moscow on Sunday if they make it out in time. "Hopefully useful. If not, perhaps it will be in a future situation".