All 12 boys and their coach who became trapped in a flooded Thai cave more than a fortnight ago have been rescued, the Navy SEALs announced on Tuesday, completing an astonishing against-the-odds rescue mission that has captivated the world.

The Thai SEALs and elite foreign divers extracted the final batch of four boys, plus the 25-year-old coach, on Tuesday afternoon via a perilous escape route that required them to squeeze through narrow, water-filled tunnels.

"All 12 'Wild Boars' and coach have been extracted from the cave," the SEALs said in a Facebook post.

"All are safe," they added, signing off with what has become their trademark "Hooyah" to celebrate the successful extractions of the other boys over the previous two days.

The 12 boys, aged from 11 to 16, and their coach, ventured into the Tham Luang cave in mountainous northern Thailand on June 23 after football practice and got caught deep inside when heavy rains caused flooding that trapped them on a muddy ledge.

They spent nine harrowing days trapped in darkness until two British divers found them, looking gaunt but otherwise offering smiles to the divers and appearing to be in remarkably good spirits.

But the initial euphoria at finding them dissipated as authorities struggled to devise a safe plan to get them out, with the shelf more than four kilometres deep inside the cave and the labyrinth of tunnels leading to them filled with water.

Authorities mulled ideas such as drilling holes into the mountain or waiting months until monsoon rains ended and they could walk out, with the rescue chief at one point dubbing the efforts to save them "Mission Impossible".

With oxygen levels in their chamber falling to dangerous levels and monsoon rains threatening to flood the cave up above the ledge where the boys were sheltering, rescuers decided on the least-worst option of having divers escort them out through the tunnels.

The escape route was a challenge for even experienced divers. The boys had no previous diving experience so the rescuers trained them to use a mask and breathe underwater via an oxygen tank.

One fear had been that they would panic while trying to swim underwater, even with a diver escorting them.

The death of a former Thai Navy SEAL diver who ran out of oxygen in a flooded area of the cave on Friday underscored the dangers of the escape route.

The ups and downs of the rescue bid entranced Thailand and also fixated a global audience, drawing support from celebrities as varied as United States President Donald Trump, football star Lionel Messi and tech guru Elon Musk.

Health concerns

Now they are out, concerns are set to focus on the physical and mental toll of the ordeal.

Experts warned that drinking contaminated water or otherwise being exposed to bird or bat droppings in the cave could lead to dangerous infections.

They also said counselling would be needed to deal with the psychological trauma of spending so long not knowing whether they were going to survive.

But there were some promising initial signs.

Medical chiefs reported on Tuesday morning that the eight boys rescued on Sunday and Monday were in relatively good mental and physical conditions.

"All eight are in good health, no fever... everyone is in a good mental state," Jedsada Chokdamrongsuk, permanent secretary of the public health ministry, said before all 13 had been rescued.

Nevertheless, the boys would remain in quarantine in hospital until doctors were sure they had not contracted any infections from inside the cave.

Even before the final rescues, tributes began for the courage of the boys and their ability to survive the ordeal.

"I cannot understand how cool these small kids are, you know? Thinking about how they've been kept in a small cave for two weeks, they haven't seen their mums," Ivan Karadzic, who runs a diving business in Thailand and has been involved in the rescue mission, told the BBC.