UPDATE: CNN reports that a former Thai Navy diver has died due to a lack of air while attempting to return to a commend center deep underground around 2 p.m. Thursday ET.

Former Sgt. Saman Kunan, an ex-SEAL, had volunteered to help rescue the 12 boys and their coach.

(CNN contributed to this report).

Original Story: A Thai provincial governor says all 12 boys and their coach have been found alive in the cave where they went missing over a week ago in northern Thailand.

Chiang Rai Gov. Narongsak Osatanakorn said late Monday, "We found them safe. But the operation isn't over."

Anmar Mirza, the U.S. National Cave Rescue Commission coordinator, says the primary decision is now one of whether to try to evacuate them or to supply them in place.

He says "supplying them on site may face challenges depending on how difficult the dives are. Trying to take non-divers through a cave is one of the most dangerous situations possible, even if the dives are relatively easy."

He says that "if the dives are difficult then supply will be difficult, but the risk of trying to dive them out is also exponentially greater."

The boys, aged 11 to 16, and their 25-year-old coach went missing when flooding trapped them after entering the Tham Luang Nang Non cave in Chiang Rai province on June 23.

The SEALs' Facebook page said that since Sunday night, the divers had reached a bend where the half-mile-long passage splits in two directions. The divers were aiming for a sandy chamber on higher ground in the cave, where they believe the group would be safe.

On Monday, they again employed the methodical, safety-first approach to make it through the passageway.

In addition to the divers, teams have been working to pump out water as well as divert groundwater. Other efforts have focused on finding shafts on the mountainside that might serve as a back door to the blocked-off areas where the missing may be sheltering.

Teams have been combing the mountainside looking for fissure that might lead to such shafts. Several have been found and explorers have been able to descend into some, but so far it is not clear whether they lead to anywhere useful.

"These are challenging conditions and there's a lot of consideration for safety as well as, the environment outside is contributing to the environment inside," said U.S. Air Force Capt. Jessica Tait, part of a 30-strong U.S. military team assisting in the search operation, referring to the rain that has been flooding the cave. "So I'd say, yeah, it's an accurate statement that it's challenging."

(The Associated Press, CBS News contributed to this report.)