The two are likely opponents in the town's upcoming mayoral election in May.
Gonzalez was released from jail after posting a $1,000 bond and has filed a lawsuit against Zarate accusing him of making a false accusation for political gain.
Jail records did not list an attorney for Gonzalez, a jail spokesman told The Associated Press.
Starr County attorney Victor Canales, who would not disclose information from the complaint until it is filed next week, said he and a justice of the peace had sufficient evidence to issue a warrant for the mayor's arrest.
"It's political -- it's all political," Gonzalez said. He also said all the public officials in Starr County were "like a bunch of used nails -- they're crooked."
La Grulla is a U.S.-Mexico border town about 220 miles south of San Antonio.
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