Gay Rights Groups to Morgan -- We DEMAND Apology

TMZ spoke with Jarrett Barrios -- the President of the Gay and Lesbian Alliance Against Defamation -- who tells us the organization is investigating the situation, and if the reports are true, "We call on him to remove these violently anti-gay remarks from his show and send a strong message that anti-gay violence is not something to joke about."

The Human Rights Campaign is equally upset -- telling us, "Hateful remarks that mock youth suicides and the very real emotional and sometimes physical bullying LGBT kids face on a daily basis have no place in a comedy routine.”