A 1967 concert tour featured performances with the Łodz and Szczecin Philharmonics. He returned to Mexico in 1969. His debut as a conductor was in the Palacio de Bellas Artes in 1969 with the Xalapa Symphony Orchestra. In 1970, he made a series of piano recordings for the Polish and Salzburg Broadcast Companies. In April 1971, he was named director, conductor, and founder of the State of Mexico Symphony Orchestra (OSEM). He continued in the post until 1983. He then was music director of the Mexico City Philharmonic Orchestra from 1983 to 1989.
Outside of Mexico, in 1984, Bátiz was named guest conductor of the Royal Philharmonic Orchestra. In 1990, he resumed his directorship of the OSEM, remaining until 2017; Bátiz then stood down as music director, nominally for health reasons related to Parkinson's Disease.
Throughout his career, Bátiz has received numerous awards. These include La primera Presea Bienal in Art from the State of Mexico Confederation of Professionals, Rome's International Gold Mercury award (the first given to a Latin American artist), and the Jose Marti and Tlatelolco's Eagle medals. In 1986, Brazil awarded him the Rio Branco medal for making the first digital recording of the nine Bachianas Brasileiras by Heitor Villa-Lobos. The Mexican Union of Theatrical and Musical Broadcasters named him the most distinguished artist of the year four times (1971, 1981, 1983, and 1996). In 1991, he received the Mozart medal given by the Domecq Cultural Institute. In 1995, he won the “State of Mexico” Prize. In 1994, because of his contribution to the musical culture of the State of Mexico and the musical world, he received the Sor Juana Ines de la Cruz award for Arts and Letters. In recognition of his achievements, he has been declared Mexiquense Destacado, or “Outstanding Mexican.”