Bangkok(CNN) Navy divers are searching a flooded cave for 12 missing boys in northern Thailand, three days after they're believed to have ventured inside with their soccer coach.

As search teams pushed deeper into Tham Luang Nang Non Cave in Chiang Rai on Tuesday, hopes remained high that the boys and their coach would survive the ordeal.

"We are still optimistic they are all alive," Deputy Prime Minister Prawit Wongsuwon told the Bangkok Post. "Even though they may not have anything to eat, they should have water to drink."

Officials believe the local soccer team crawled into the cave through a narrow 15-meter long channel, leading to a series of caves up to three kilometers (1.86 miles) long.

Rising waters then blocked the path, which is about as wide as a single person, leaving the group stuck inside the cave network, Kamolchai Kotcha, an official with Thailand's national parks authority, told CNN on Monday.

"We have been working almost 24 hours but there are many limitations, the caves are pitch dark and very low level of oxygen in some areas, and scattering rains just made our task more difficult," said Kotcha.

Officials search for a group of 13 trapped in a Thai cave.

Park officials, local police and 17 members of the SEAL diving team from the Royal Thai Navy were deployed to assist in the search and rescue efforts.

A post on the Thai Royal Navy SEAL Facbook page Monday afternoon stated: "It is still drizzling (and) water level is rising. Handprints were found around cave's wall. But we still cannot locate the kids. Rescue operation continues."

An image posted said that SEAL divers have to dive to a depth of five meters to access the main chamber, where the missing boys are believed to be located.

The Thai Navy SEALs shared this image on Facebook with the caption, "Divers have to dive 5 meters deep to enter the main chamber." A portion of the photo was obscured by the Thai Navy SEALs.

A post later that evening said that the dive team had to temporarily suspend their search due to flooding.

The search resumed on Tuesday, with electric cables and ventilation hoses being laid in the cave, the Bangkok Post reported.

Search teams are battling rising water levels by pumping out water from both the cave and the Nam Phu reservoir, which lies underneath.

Rescue teams gather at the entrance of a deep cave where a group of boys went missing in Chiang Rai, northern Thailand.

Navy chief Admiral Naris Prathumsuwan told the Post that he was most worried that the boys were suffering from hunger and exhaustion.

Thai King Maha Vajiralongkorn Bodindradebayavarangkun has also expressed concern for the team and support for their families.

The 13 people, all males from Chiang Rai, have been missing since 1 p.m. local time Saturday, when a park officer spotted something amiss -- bicycles parked idly by the entrance to the cave, despite it being off-limits.

The caves are located in a well-known spot for local explorers and tourists in the northern province of Chiang Rai's Mae Sai District.

Northern Thailand is famous for its remote and untouched caves, which draw visitors from around the world.