Zimmerman is charged with second-degree murder in the teenager's death.
He made the statement Wednesday in an interview with Fox News host Sean Hannity.
When asked to explain what he meant when he told a police dispatcher he was following Martin, the neighborhood watch volunteer said he was trying to keep an eye on Martin to tell police.
Zimmerman says after he got out of his car, Martin was next to him. Zimmerman says he looked down, then looked up and Martin punched him and broke his nose.
He says as the two were struggling, Martin said "you're going to die tonight." He says Martin also reached for the gun that Zimmerman always carries.