MAE SAI, Thailand—Authorities working to rescue a teenage soccer team from a flooded cave in northern Thailand said they would withdraw nonessential personnel from a staging area in the cave over concerns that air quality could drop to a dangerous level.

“Today we made the decision to withdraw some unnecessary people from chamber three,” said Gov. Narongsak Osottanakorn. That area of the cave is being used as a base for rescue workers, and he said their breathing has lowered the level of oxygen and raised the level of carbon...