Two more boys left the Tham Luang Nang Non cave complex a short time later and were transferred to a medical facility on site, followed soon after by a fourth boy, according to the eyewitness, who is stationed at the entrance to the cave.
"The divers that were assembled from many countries are proud to have conducted this operation until its success", Narongsak added.
A press briefing was to be held shortly.
The four boys pulled from the cave Sunday in an urgent and unsafe operation that involved them diving through the cave's dark, tight and twisting passages were happy and in good health, authorities said.
It takes around eight hours for divers and rescuers to get them out.
The world has been hooked on the fate of the group of Thai boys trapped in a cave and the heroic attempts to rescue them. They have not been reunited with their families yet due to infection concerns. The 12 boys and their coach were trapped in the cave for two weeks.
Although weak, they are largely in good health, authorities have said.
A daring rescue operation the likes of which the world has never seen is now underway with the participation of a team of Thai and global divers. They became trapped in the cave after heavy rain flooded the passageways inside.
They were finally found by a team of British divers and have since been receiving oxygen and food while waiting to be brought out.
Rescue mission chief Narongsak Osotanakorn said Monday's rescue operation was two hours shorter than the previous one after authorities reviewed the process to make it sharper.
"If everything turns out as we've expected, whether it be the weather or readiness of the rescue team, there should be nothing to worry about", Chalongchai said.
Change Mai governor Narongsak Osottanakorn said on Monday that the rescued boys' identities were being protected out of respect for the families of those still trapped inside the cave.
A truck carrying oxygen tanks arrives outside the Tham Luang cave complex, where 12 schoolboys and their soccer coach are trapped inside a flooded cave, in the northern province of Chiang Rai, Thailand, July 8, 2018.
The dramatic and unsafe rescue at the Tham Luang cave in the northern province of Chiang Rai was launched on Sunday and four boys were brought out that day.
The names of those rescued have not been released.
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.
Narongsak said that experts told him new rain could shrink the unflooded space where the boys are sheltering to just 108 square feet.
The cave complex is off-limits during the rainy season, which usually runs from May to October, when downpours can quickly flood it. Relatives said the boys had been inside the complex during the dry season.
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