A navy spokesman said the search for the vessel would continue with international assistance but ruled out the chance of finding any survivors.
The ARA San Juan had a seven-day supply of air when it reported its last position on November 15.
The crew had been ordered to return to a naval base in Mar del Plata after reporting water had entered the vessel through its snorkel.
Argentine Navy spokesman Enrique Balbi said: “More than double the number of days have passed where it would have been possible to rescue the crew.
“We will continue the search. There will not be people saved.”
He said the navy was unable to confirm the fate of the crew and no evidence of a shipwreck had been found in the search area.
The decision to end the rescue mission has dismayed relatives who were already angered by Argentine defence chiefs’ handling of the tragedy.
A huge sea and air hunt was launched for for the San Juan, a German-built, diesel- and electric-powered submarine which was launched in 1983.
Some relatives have questioned authorities for letting the crew navigate on an ageing submarine – criticism that has highlighted the armed forces’ dwindling resources since the end of a military dictatorship in the 1980s.
Authorities have said the level of maintenance, not the age, was what mattered, and that the vessel was in good condition.
It received a midlife upgrade in 2009 in which its four diesel engines and electric propeller engines were replaced, according to the specialist publication Jane’s Sentinel.
Recent reports suggested water had previously entered the snorkel of the submarine and caused its battery to short-circuit before it went missing.