Martinez, who joined Inter Milan from Racing earlier this summer, and Simeone, the Spain-born striker who plays for Fiorentina, are included up front alongside Paolo Dybala, Angel Correa and Cristian Pavon.
Mauro Icardi, the Inter striker who was surprisingly left out of Argentina's World Cup squad, also returns, but there is no place for Gonzalo Higuain, Sergio Aguero or Angel Di Maria.
Lionel Messi was left out after requesting an unspecified time out from international duty.
Only nine of the 23 players who went to the Russia World Cup are included for the games against Guatemala in Los Angeles on Sept. 7 and Colombia in New Jersey four days later.
Franco Martinez, the Sevilla midfielder who played two friendlies for Italy in 2015, is among the new names in the 29-man squad, as is Gremio centre-half Walter Kannemann.
Interim coach Lionel Scaloni also gave call-ups to uncapped Stuttgart midfielder Santiago Ascacibar and Real Sociedad goalkeeper Gerónimo Rulli.
Argentina disappointed in Russia, drawing with Iceland, losing to Croatia and then qualifying for the knock-out stages with a win over Nigeria.
However, they were dispatched by eventual winners France 4-3 in the last 16 and coach Jorge Sampaoli left soon after.
Goalkeepers: Franco Armani (River), Geronimo Rulli (Real Sociedad), Sergio Romero (Manchester United).
Defenders: Fabricio Bustos (Independiente), Gabriel Mercado (Sevilla), German Pezzella (Fiorentina), Ramiro Funes Mori (Villarreal), Alan Franco (Independiente), Nicolas Tagliafico (Ajax), Walter Kannemann (Gremio), Leonel Di Plácido (Lanus), Eduardo Salvio (Benfica), Marcos Acuna (Sporting Lisbon).
Midfielders: Leandro Paredes (Zenit), Santiago Ascacibar (Stuttgart), Rodrigo Battaglia (Sporting Lisbon), Gonzalo Martinez (River), Giovani Lo Celso (PSG), Franco Cervi (Benfica), Maxi Meza (Independiente), Matias Vargas (Velez), Franco Vazquez (Sevilla), Exequiel Palacios (River).
Forwards: Angel Correa (Athletico Madrid), Lautaro Martinez (Internazionale), Mauro Icardi (Internazionale), Giovanni Simeone (Fiorentina), Cristian Pavon (Boca Juniors), Paulo Dybala (Juventus).
(Reporting by Ramiro Scandolo; Writing by Andrew Downie; Editing by David Holmes)
