Porter, who previously won a Tony and Grammy for his role in Broadway's "Kinky Boots," continued with a quote from writer James Baldwin.
"'It took many years of vomiting up all the filth that I had been taught about myself and halfway believed before I could walk around this Earth like I had the right to be here,'" Porter read before adding, "I have the right. You have the right. We all have the right."
Porter went on to thank his family, manager Bill Butler, "Pose" casting director Alexa Fogel, series co-creator Ryan Murphy and his co-stars.
"Oh, my goodness," Porter said. "We are the people. We as artists are the people that get to change the molecular structure of the hearts and minds of the people who live on this planet. Please don't ever stop doing that. Please don't stop ever telling the truth. I love you all."
He then quipped: "They're telling me to please stop. God bless you."
Other nominees in the category included actors Jason Bateman, "Ozark"; Kit Harington, "Game of Thrones"; Bob Odenkirk, "Better Call Saul"; Milo Ventimiglia, "This Is Us"; and Sterling K. Brown, also of "This Is Us."
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– The Associated Press contributed to this report.