Expectations in Argentina are enormous for the team to win the South American championship and its first major title in 18 years.
Argentina is the host country and Manchester City striker Carlos Tevez said it would be a ''failure'' if two-time World Cup champion Argentina failed to win it.
''It won't be a failure,'' Batista replied on Wednesday. ''We are obliged to win it - we're in Argentina. Expectations are big and Argentina, like in everything, is obliged to be successful.''
Batista missed the early part of the training after being delayed in Brazil because of flights grounded by ash from a Chilean volcano.
Batista and a core of young players were returning from two matches abroad - a 4-1 loss at Nigeria and a 2-1 loss at Poland.
Argentina's top players such as Lionel Messi, Tevez and Javier Mascherano made the first practice, which was conducted by assistant coach Alejandro Tocalli.
Argentina opens the Copa America on July 1 against Bolivia, and is expected to reach the final and face Brazil.
Batista is also feeling the heat from Julio Grondona, the embattled president of the Argentine Football Association.
Grondona charged Batista with ''auctioning off the prestige'' of the national team following the lopsided loss last week at Nigeria, in which Batista fielded only second-line players. Three days later, the same squad lost 2-1 to Poland.
Grondona, president of AFA for 32 years, has his own problems.
The leading daily La Nacion last week called for him to resign, questioning his leadership after acknowledging recently that he made sure there was no drug testing for a World Cup playoff in 1993 between Argentina and Australia.
Daniel Passarella, who coached Argentina and was a member of its World Cup-winning teams in 1978 and 1986, also called last month for Grondona to step down.
Grondona has been accused of looking the other way at hooligan violence at club matches. A nonprofit organization says 256 people have died in football-related violence in Argentina since 1924 - 13 in just the past year. A match last weekend was suspended when a police officer was wounded in a shootout between rival hooligan gangs. The wound was not life-threatening.
FIFA, the governing body of football, is also investigating Argentina's 4-1 loss to Nigeria with betting patterns suggesting it was targeted by match-fixers. Neither AFA nor Argentine players have been implicated.