Rocker said he was with his girlfriend on Sunday at Breadwinners Cafe & Bakery when some customers began badgering and pestering him.
"It seemed as if they were trying to bait me with suggestive comments," Rocker said in the statement.
Richard Garcia, who waited on Rocker and his girlfriend, said the ballplayer was not provoked. Garcia said Rocker called a male couple sitting at a nearby table "fruitcakes" as he got up and left.
"That's nothing someone should hear from somebody who's supposed to be a role model," Garcia said in a story in The Dallas Morning News' Tuesday edition. "Just because you're a superstar, that still does not license you to say that."
Rocker said he finished his meal and got up to leave. Then, he said, the unidentified patrons followed him out of the restaurant, located in a predominantly gay neighborhood, and made an obscene gesture.
"At that point, I admit I was angry and said some things I probably should not have said, but I wanted to make it clear their attentions were unwelcome," he said.
Rangers spokesman John Blake told The Associated Press that the remarks were anti-gay in nature but Rocker's specific comments were unknown.
"I didn't ask him exactly what he said," Blake said.
Rangers manager John Hart issued a separate statement, saying: "John told me he did lose his temper after some customers badgered him, made suggestive comments and then followed him and his girlfriend out of the restaurant."
The Rangers traveled to Detroit on Monday and couldn't be reached for further comment.
Rocker remains reviled by some for disparaging remarks he made about gays and minorities in a Sports Illustrated interview before the 2000 season.
"Of course, we do not condone name-calling," Hart said. "Our general advice to players is to leave a hostile public situation. And that's what he did. It is my opinion that this is a personal issue between John and the people in the restaurant."
In 1999, Rocker saved 38 games and pitched in the World Series for Atlanta. He saved 24 games in 2000 and 23 last season before the Braves traded him in June 2001 to Cleveland.
Rocker, on the disabled list since July 4 because of a left shoulder injury, traveled with the Rangers to Detroit.
"He's human but he should know better," Breadwinners manager Feletia Lee told Dallas-Fort Worth television station KDFW. "There are a lot of people here who aren't going to go to any Rangers games again.
"I'm not going to go. I can't support them. That is just uncalled for."