MAE SAI, Thailand -- Rescuers found all 12 boys and their soccer coach alive deep inside a partially flooded cave in northern Thailand late on Monday, more than a week after the team disappeared and touched off a desperate search that drew international help and captivated the nation.

Chiang Rai provincial Gov. Narongsak Osatanakorn said the 13 were in the process of being rescued, but he cautioned that they were not out of peril yet.

"We found them safe. But the operation isn't over," he said in comments broadcast nationwide.

Rescue divers had spent much of Monday making preparations for a final push to locate the lost soccer players, ages 11 to 16, and their 25-year-old coach. They disappeared when flooding trapped them after entering the Tham Luang Nang Non cave on June 23.

Rescue workers pump water from the cave in Thailand where a youth soccer team went missing over a week ago. Royal Thai Army/EPA

Anmar Mirza, a leading American cave rescue expert, said many challenges remain for the rescuers. He said the primary decision is whether to try to evacuate the boys and their coach or to supply them in place.

"Supplying them on site may face challenges depending on how difficult the dives are," Mirza, coordinator of the U.S. National Cave Rescue Commission, said in an email. "Trying to take non-divers through a cave is one of the most dangerous situations possible, even if the dives are relatively easy. That also begets the question: If the dives are difficult then supply will be difficult, but the risk of trying to dive them out is also exponentially greater."

Prime Minister Prayuth Chan-ocha thanked the international experts and rescuers who helped locate the missing for their "tremendous efforts."

"The Royal Thai Government and the Thai people are grateful for this support and cooperation, and we all wish the team a safe and speedy recovery," Prayuth's office said in a statement.

Thai Navy SEAL divers and rescue workers from other countries made initial progress through the narrow passageway early Monday after passing through a key chamber on Sunday where high, murky waters had previously blocked their progress.

Gov. Narongsak earlier said the passageway the divers made their way through goes upward in some places and downward in others and is extremely narrow, making it difficult for divers and their gear to fit through.

Divers have been stymied repeatedly by rising water that forced them to withdraw for safety reasons. When water levels fell Sunday, the divers went forward with a more methodical approach, deploying a rope line and extra oxygen supplies along the way.

The Facebook page for the SEALs 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.

Narongsak explained earlier Monday that fixing rope lines and deploying oxygen tanks along their route will allow the divers to operate.

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.

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.

Experts in cave rescues from around the world had gathered at the site. An official Australian group has followed a U.S. military team, British cave experts, Chinese lifesaving responders and several other volunteer groups from various countries.

"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-member 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."