Lletget posted a video on his Instagram account of him using the slur in Spanish while walking with Galaxy teammate Julian Araujo at a practice session. Lletget appeared to jokingly slap Araujo on the neck from behind before using the slur.
Lletget deleted the video shortly afterward. In a statement to OutSports, Lletget said he "messed up" for using the slur.
"I have taken down a video from my Instagram story but want to address its impact and not hide from this. I take full responsibility and ownership on what was an extremely poor and ill-thought phrase and have no excuse for my actions. I am sorry and know the pain that this term has caused for so many.
"I want to be part of the solution -- not part of the problem -- and continue to be an advocate and an ally for the LGBTQ+ community. Those who know me know my character and heart. I will remain outspoken in my support and advocacy. My error doesn't change that.
"Thanks for your accountability. I need to do and be better."
The Galaxy stated: "The L.A. Galaxy do not condone homophobic or derogatory language of any kind. The club stands with the LGBTQ+ community and will address this matter internally."
MLS said it was aware of the incident and it would open an investigation.
"Major League Soccer is committed to providing an environment in which all individuals are treated with dignity and respect, and we have no tolerance for discrimination and prejudice of any kind. We are aware of the use of a homophobic slur by an LA Galaxy player. MLS has begun a formal investigation regarding the language used by the player and more information will be provided as soon as it becomes available," the league statement said.
Lletget has played for the Galaxy since 2015, with 151 appearances for the team. Most recently, he appeared for the USMNT during their two March friendlies.