The "hydro-acoustic anomaly" was produced just hours after the navy lost contact with the ARA San Juan on November 15, said Enrique Balbi, a navy spokesperson.
According to the Argentine navy spokesman, despite the magnitude of the efforts made, it has not been possible to locate the submarine.
"I don't understand this arbitrary and unjustified decision", Luis Tagliapietra, the father of 27-year-old crew member Alejandro Tagliapietra, told local TV.
"Navy spokesman, Enrique Balbi stated that the search for the submarine had been extended to more than double the number of days that determine the possibilities of rescuing the crew". "We will continue the search. there will not be people saved".
Officials have said the submarine had enough air for seven to 10 days when submerged.
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Some relatives of the crew broke into tears after they received the news.
The announcement was made Thursday, a full 15 days after an explosion is believed to have sent the ill-fated vessel to the depths of the Atlantic ocean off the coast of Patagonia.
The Argentine navy said it could have been the sound of the submarine imploding. The captain later communicated by satellite phone that the problem had been contained, the navy says.
The final message from the submarine reported a leak of seawater and the beginnings of a battery fire, but navy Adm. Gabriel Gonzalez said he didn't consider the incident an emergency.
The search for the San Juan has employed some of the latest technology in one of the largest efforts of its kind.