Gerado Martino departs just days after Argentina lost on penalties to Chile in the Copa America final.
The 53-year-old in a statement indicated that he quit because of a “lack of decisions” at the head of the Argentine FA (AFA) and “serious problems” in selecting a squad for the Olympics.
The Argentine managed his country from August 2014, after previously coaching Barcelona.
Last month’s Copa America defeat was the second time Argentina finished runner-up to Chile in the competition during Martino’s reign.
A host of other leading Argentina players are reportedly close to quitting the national team, although there has been no confirmation of further retirements.
Martino has also struggled to choose an 18-man squad for the Olympic football tournament in Rio, which starts on 3 August – two days before the Games formally commence.
Argentine media says Martino is frustrated clubs are unwilling to release player in time for Rio. At present there are only nine players in Argentina’s Olympic squad, and the president of the country’s Olympic committee has hinted he may not send a team.
The Argentine FA has also been struggling amid a power vacuum that followed the death of long-time president Julio Grondona in 2014.
The Argentine FA has been placed under the administration of a Fifa committee in order to prepare it for new presidential elections in 2017.
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