Tevez was left out of the squad that played Portugal in Geneva last month having withdrawn from a November game against arch-rivals Brazil only to play for City four days later.
Argentine Football Association president Julio Grondona cited that as the reason for his being dropped.
Argentina meet United States in New Jersey on March 26 and Costa Rica, now coached by Argentine former Mexico trainer Ricardo La Volpe, in San Jose three days later.
Injuries to players including Inter Milan striker Diego Milito have allowed Batista to call up others like Benfica forward Eduardo Salvio, who won his only cap under former coach Diego Maradona in 2009.
With Real Madrid's Fernando Gago injured, Porto midfielder Fernando Belluschi, who won his second cap in 2007, earned a recall, as did World Cup squad member Mario Bolatti having moved from Fiorentina to Internacional of Brazil this year.
Players whose Argentine clubs have league or Libertadores Cup commitments on or close to the match dates have also been left out of the 24-man list.
Batista's team have won four and lost one of their five friendlies since he took over from Maradona after the 2010 World Cup finals.
Goalkeepers: Sergio Romero (AZ Alkmaar), Mariano Andujar (Catania), Adrian Gabbarini (Independiente)
Defenders: Javier Zanetti (Inter Milan), Pablo Zabaleta (Manchester City), Nicolas Burdisso (AS Roma), Nicolas Otamendi (Porto), Gabriel Milito (Barcelona), Marcos Rojo (Spartak Moscow), Ezequiel Garay (Real Madrid), Federico Fazio (Sevilla)
Midfielders: Javier Mascherano (Barcelona), Mario Bolatti (Internacional), Esteban Cambiasso (Inter Milan), Fernando Belluschi (Porto), Ever Banega (Valencia), Angel Di Maria (Real Madrid), Javier Pastore (Palermo), Lucas Biglia (Anderlecht), Jose Sosa (Napoli)
Forwards: Lionel Messi (Barcelona), Ezequiel Lavezzi (Napoli), Nicolas Gaitan (Benfica), Eduardo Salvio (Benfica)
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