Lletget fought back tears and said he will work with Major League Soccer to try to become an ally for the LGBTQ+ community.
"I messed up and I'm trying to take full responsibility for it," Lletget said. "I said a word that shouldn't have been said. And although there's been a lot of discussion and debate about the meaning of the word because of different dialects in Spanish and cultures, the truth is it's a harmful word and it shouldn't have been said."
MLS previously announced it was aware of the situation and would begin a formal investigation. Lletget said he has been in contact with the league office but has not been notified of any possible disciplinary action ahead of the team's season opener against Inter Miami CF on Sunday.
"Moving forward, I really do want to do my part," Lletget said. "I hate that this door has been opened this way, but I've always wanted to be involved in social causes and I've always wanted to be an ally. I hope there's a silver lining and now the door is open, and I'm more than happy to walk through it and take it on and help and help different communities."
Lletget used the Spanish slur as he slapped teammate Julian Araujo on the back of the neck outside a recent Galaxy training session and deleted the video from his Instagram account shortly after posting it.
"This was a poor decision on my end and it was a moment of just pure stupidity," Lletget said. "I'm a human, I made a mistake and that's simply what happened. But now I want to rectify that."
Lletget has played for the Galaxy since 2015, with 151 appearances for the team. Most recently, he appeared for the USMNT during its two March friendlies.