Clinton then mentioned Texas Sen. Ted Cruz, which drew hisses and boos from the crowd gathered inside the grand ballroom of the Mayflower Hotel, and went on to challenge him to join her at a gay pride parade.
"Ted Cruz slammed a political opponent for marching in a pride parade. He clearly has no idea what he's missing. Pride parades are so much fun. I was marching in them back when I was first lady. You should join sometime Senator, come on," she said.
Both Carson and Cruz have said they believe marriage is between a man and a woman. ABC News has reached out to their campaigns for comment to Clinton's remarks.
"Hillary would have everyone believe she's been in favor of marriage equality since the fall of the Roman Empire," Carson campaign spokesman Doug Watts said. "When she's not lying, she's spinning!"
Cruz's campaign did not respond to ABC News' request for comment.
Clinton, who supports same-sex marriage, also took a forceful stance on transgender issues during her remarks, and called for the military to allow transgender people to serve openly.
"We need to say with one voice that transgender people are valued, loved, and one of us," she said. "Transgender people are still banned from serving. That is an outdated rule – especially since you and I know that there are transgender people in uniform right now. They’re just keeping this core part of their identities under wraps because they are so committed to defending our nation. They shouldn’t have to do that. That’s why I support the policy review that Defense Secretary Carter recently announced at the Pentagon. And it’s why I hope the United States joins many other countries that let transgender people serve openly."
She later called out the Republican presidential candidates for ignoring the issue all together.
"See if you are ever in a forum with any of them, if you can get them to say the word transgender," she said.
In addition, Clinton called on Congress to pass the Federal Equality Act. And she said she would upgrade dishonorable discharges of service members who were forced out of the military in years past for being gay.
Clinton, who announced her support of same-sex marriage in March 2013 in a video produced by the Human Rights Campaign, today thanked the organization for the work it has done to help get it legalized in all 50 states.
"The people here today deserve a lot of credit for making it happen. You've helped change a lot of minds, including mine, and I am personally very grateful for that," she said.
There were plenty of jokes at the event playing on the fact that Clinton and the Human Rights Campaign share the same initials: HRC.
During the opening of her remarks, Clinton said, "It is great to be back with the other HRC ... there’s no one else I’d rather share my initials with.”
And later, when promising to fight for LGBT rights as president, she said this: "That’s a promise, from one HRC to another."