Some relatives of the crew broke into tears after they received the news.
"I don't understand this arbitrary and unjustified decision," Luis Tagliapietra, the father of 27-year-old crew member Alejandro Tagliapietra, told local TV. "It's unusually cruel. Every day, it's a new blow. I'm destroyed."
The Navy has said the vessel's captain reported that water entered the snorkel and caused one of the submarine's batteries to short circuit. The captain later communicated by satellite phone that the problem had been contained, the Navy says.
Some hours later, an explosion was detected near the time and place where the San Juan was last heard from. A navy spokesman said this week that the blast could have been triggered by a "concentration of hydrogen" caused by the battery problem reported by the captain.
The San Juan, a German-built diesel-electric TR-1700 class submarine, was commissioned in the 1980s and was most recently refitted in 2014.