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The rescuer passed out and died from a lack of oxygen while on a mission supplying oxygen canisters, authorities told the Associated Press.
SEAL commander Arpakorn Yookongkaew said at a news conference the rescuer was working as a volunteer and efforts to revive him failed, adding, "Despite this, we will continue until we accomplish our mission."
The BBC identified the diver as 38-year-old Saman Gunan. His death was confirmed around 2 a.m. local time.
A post to the Facebook page of the Thai navy SEALS mourning Gunan read in part:
"He resigned from the military and had worked as a patrol officer at the Suvarnabhumi Airport since 2006. He was a very capable SEAL and a triathlete who liked adventure sports. Although he resigned from the unit, he still loved and had a good connection with all the SEALs. ... Even the last part of his life, 1st Petty Officer Saman left us and this world while working with the SEAL brothers who are also trying to go forward and complete the mission as planned.
"His determination and good intention will always be in the heart of all SEAL brothers. Today, you get some good rest. We will complete the mission for you."
The death of an experienced diver highlights just how difficult it may be to extract the 13 who are trapped. One escape plan called for having the boys scuba dive to safety.
Authorities are trying to pump water from the flooded cave, in which 12 boys and their coach have been trapped since June 23. More rains are forecast for the region and could complicate further rescue efforts.
"The environment inside the cave is challenging," Yookongkaew said. "We can no longer wait for all conditions [to be met] because circumstance is pressing us. We originally thought the boys can stay safe inside the cave for quite some time, but circumstances have changed. We have limited amount of time."
ABC News' Joohee Cho, Matt Gutman, Aicha El Hammar, James Longman, Matt McGarry, Scott Shulman and Robert Zepeda contributed to this report.