The discovery of the missing group by British divers late on Monday has brought relief and joy to their families and people around the world.
The navy is also seeking permission to posthumously promote Saman, who was a petty officer first class when he left the unit, Channel News Asia reports.
Another navy official said he didn't believe the man's oxygen tank ran out.
His diving partner tried performing CPR on him but was unable to revive him.
Authorities have confirmed the diver's death was caused by lack of oxygen, and he died while making his way out of the cave complex where the group is trapped.
"A former Seal who volunteered to help died last night about 2am", Chiang Rai deputy governor Passakorn Boonyaluck told reporters at the site, calling it "sad news". "His job was to deliver oxygen". Officials said the diver would be given royally-sponsored funeral rites including a military funeral at the Satthahip Navy Base in Pattaya, and then in his hometown in the northern Thailand province of Roi Et.
"They may have some belief that their techniques are effective for groundwater drainage, but anything that is not in the plan must be discussed with us first", Narongsak told Thai media.
During a press conference early Friday morning, Thai Navy SEAL commander Rear Adm. Arpakorn Yookongkaew said there is "limited amount of time" to rescue the group.
"We have been trained to always be dealing with risks", he said.
"We won't let his life be in vain".
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Asked how the boys could make it out safely if an experienced diver could not, Apakorn said they would take more precautions with the children. The boys are said to be too weak from malnutrition to even make the trek.
Ake, the boys' coach, wrote a letter to relatives, saying: "To my grandma, I'm ok, I'm fine". They were found on July 2, but because of the difficulty of their position in the cave, they can't be rescued yet.
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The Navy source said boys' biggest challenge would be a 200m stretch of the completely flooded cave that made up part of the 600m section between "Pattaya Beach" and chamber three.
Asked at his news conference about bringing the boys out underwater, Chiang Rai Governor Narongsak Osatanakorn replied: "Not today because they can not dive at this time".
Narongsak said experts, who themselves have made the hard journey, were teaching them the rudiments of diving, but that the boys were not yet capable of an arduous and complicated mission. Saman Gunan lost consciousness underwater during an overnight operation delivering extra air tanks inside the cave, along the treacherous route divers take to get to the trapped soccer team.
The boys, who are aged 11 to 16, became cut off by monsoon flooding two weeks ago.
Rescue teams, meanwhile, have thrashed through dense forest above the cave complex, looking for a place to start drilling a rescue shaft.
Experienced divers are wary of taking out the boys through the dark and unsafe waters still in the cave, especially since they are untrained.