Teixeira called the accusation of racism "completely erroneous."
"You guys can talk to every single one of my teammates," said Teixeira, who's been hit by Padilla three times in his career and on Friday hit a go-ahead triple off the right-hander. "That's crazy, but I wouldn't expect anything else really."
Padilla declined Sunday when asked by a Red Sox official to speak to reporters through a translator. Padilla told NESN.com that Teixeira also had problems with pitcher Frank Francisco, who was in Texas when Padilla and Teixeira were teammates there.
"The things [Teixeira has] done -- against the Latinos [on the Rangers] -- he doesn't open his mouth about," Padilla told NESN.com. "He once threatened me and said he was going to hit me with a bat, and that's when we were playing on the same team. ... And then, he also had problems with Frank Francisco, our closer back then."
"We used to be friends, but then there was this incident when I hit someone unintentionally and then he got hit and then he said he would retaliate and hit me with a bat," Padilla said to ESPNDeportes.com. "I guess it escalated from there."
Teixeira disputed he made a bat threat, but a player that was with the Rangers during the time Padilla and Teixeira were there told MLB.com there was "no doubt" that it happened. That incident came at a time when Teixeira was with a team other than the Rangers, the player said.
The same player also said he never saw any racial bias from Teixeira, and never saw any enmity between Teixeira and Francisco.
"Yeah, [Padilla] had a problem for some reason with Mark Teixeira," the player said. "And he would throw at him every single time he faced him. It got to the point where Teixeira did say something like, 'If you hit me again, I'm going to come at you with a bat or whatever it was. But no one had Padilla's back.'"
As for Francisco, Teixeira alluded only to a 2004 arrest for Francisco that he said was not talked about in the clubhouse, essentially denying an outward conflict.
"We couldn't talk about it with anybody, even within the team we couldn't talk about it," Teixeira said. "And that was the only issue I would've ever seen come up."
Padilla also told NESN.com that Teixeira would "be better off playing a women's sport." Teixeira quipped in response that "women's boxing's pretty tough, so I don't know if I could handle that."
Padilla elaborated further to ESPNDeportes.com.
"[Teixeira] is always crying and complaining," Padilla said. "If he has a base hit, he cries, if he doesn't, he cries. I just meant that not even women complain as much as him."
Going forward, the two players are likely to face each other again in the second half. Yankees manager Joe Girardi said he would "definitely think about" removing Teixeira if a game were not close and he feared for his player's health.