See Caitlyn Jenner Preach Acceptance in Emotional ESPYs Award Speech

— -- Caitlyn Jenner made an emotional plea for "accepting people for who they are" as she was honored with the Arthur Ashe Courage Award at Wednesday's ESPYs in Los Angeles.

Jenner, donning a white, long-sleeve gown, acknowledged her mother, her children and ABC News' Diane Sawyer in her acceptance speech and called the past few months a "whirlwind."

She said she had never met a transgender person until the past few months, and instead dealt with her "situation" alone and in private.

"That turned this journey into an already incredible education," Jenner said.

"This transition has been harder on me than anything I could imagine," she said, adding that "trans people ... deserve your respect."

Jenner, a former Olympic superstar, said she knows the "power of the spotlight" and understands "with attention comes responsibility."

"It's about all of us accepting one another," she said.

Kendall, Kylie and Brody Jenner posed on the red carpet earlier tonight to support their famous dad.

Jenner's other children were also at the ceremony for support: Burt Jenner, Cassandra Marino and Brandon Jenner, as well as daughter-in-law Leah Jenner and step-daughters Kourtney, Kim and Khloe Kardashian, all seen in this photo posted by Kourtney:

Brody Jenner told ABC News tonight it was "such a courageous thing for her to come out" and said Caitlyn is "extremely happy."

Brody said they're all celebrating with a big family dinner.

Jenner, 65, formerly known as Bruce, revealed in April that she is woman. In June, Vanity Fair magazine released the first photo of the former Olympian since her physical transformation, as well as her name.

“Bruce has received many accolades over the years for being one of the greatest Olympians of our time but The ESPYS are honored to celebrate Bruce becoming Caitlyn," said executive producer Maura Mandt in a statement last month.

"She has shown the courage to embrace a truth that had been hidden for years, and to embark on a journey that may not only give comfort to those facing similar circumstances, but can also help to educate people on the challenges that the transgender community faces.”