The Argentine Football Association (AFA), facing an identity crisis in the national game, announced Batista had stepped down after his team were knocked out of the tournament in the quarter-finals nine days ago.
"The national teams commission has decided to rescind the contract," AFA spokesman Ernesto Cherquis Bialo told a news conference.
"Batista wasn't sacked," Cherquis Bialo said. "[Batista] put his future as the head of the national team up for consideration by the (AFA) executive committee."
Cherquis Bialo also said Argentina's August 10 friendly against Romania in Bucharest on August 10 had been cancelled.
"The coaching staff of Argentina teams at all levels are under evaluation by the national teams commission," he added.
"There are no deadlines, there´s no rush, no urgency [to name a new coach] so there will be a process of consideration and study."
Batista, 48, had been in charge for a year, initially in an interim capacity after predecessor Diego Maradona was refused a new contract following Argentina's quarter-final elimination at the 2010 World Cup finals in South Africa.
His contract was to take him to the end of the South American qualifiers for the 2014 World Cup finals in Brazil with Batista vowing to build a team around Lionel Messi, the world's best player, to win the title.
Batista, nicknamed Checho, did not promise to deliver the Copa America but said it was Argentina's obligation as hosts to win the trophy and he was confident they would, having lost to Brazil in the previous two finals.
However, Argentina struggled against tough South American opponents also preparing for the World Cup qualifiers by building their teams from the back in contract to Batista's stated aim to play in the mould of European champions Barcelona, Messi's club.
Batista, holding midfielder in the 1986 World Cup-winning team, came into the senior job via the Olympic team he steered to Argentina's second successive gold medal at the 2008 Beijing Games.
With South America's World Cup qualifiers kicking off in October, the AFA decided an overhaul critics said should have been made a year ago had to be done at once.
