Narongsak Osottanakorn, head of the rescue operation, said a team of divers went back into the cave Monday morning, local time.
"Coordination and interaction with Thai military, Thai government, and other multinational civilians and government entities remains extremely positive and effective", he said.
"Water levels are the same like the last two days", he said, adding that rescue efforts were expected to faster than they had been before.
The "Wild Boars" team became trapped on June 23 when they set out to explore the cave after soccer practice and rains flooded the tunnels. This now brings the total number of rescued boys to eight. The rescue effort is slowed somewhat by the fact that the team must replenish supplies and oxygen tanks that line the 2.5-mile route out of the cave.
"On behalf of the United States, congratulations to the Thai Navy SEALs and all on the successful rescue of the 12 boys and their coach from the treacherous cave in Thailand", he tweeted. "His sacrifice will not be forgotten".
An ambulance has been seen leaving the site of the Thai cave where divers are carrying out what they hope is a final mission to bring out four boys and their soccer coach still trapped deep inside.
So the challenge for the children lies in keeping in keeping calm while remembering the minutiae of a new skill, Foisey said.
Early tests indicate all of the boys could be suffering from lung infections, but only two of the first four boys were confirmed.
The rescue mission began on Sunday morning, almost a week since the 12 boys, aged 11-16, and their coach had been discovered on an embankment 2.5 miles (4 kilometers) inside the winding tunnels.
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.
The boys rescued so far are in good overall health despite spending two weeks in the dank cave system, said Jesada Chokedamrongsuk, permanent secretary of the ministry of public health, at a news conference in Chiang Rai.
"If, as we all hope, they are reunited with their families in the coming days and their health allows them to travel, Federation Internationale de Football Association would be delighted to invite them to attend the 2018 World Cup final in Moscow as our guests".
And, Foisey said, the boys do have one thing going for them: "I'm sure these kids were very determined to get home".
But family members have seen at least some of the boys from behind a glass barrier. "All the thirteen Wild Boars are now out of the cave", the Thai navy SEALs team, which is helping to lead the operation, said on its Facebook page.