"Music has always helped me tell my story,'' Obama said at the Staples Center in Los Angeles. "Whether we like country or rap or rock, music helps us share ourselves. It allows us to hear one another.''
Gaga told the crowd: "They said I was weird, that my look, that my choices, that my sound wouldn't work. But music told me not to listen to them.''
Jada Pinkett Smith and Jennifer Lopez also spoke and stood in solidary with Obama, Gaga and Alicia Keys, who is hosting the show.
"Yes, ladies,'' Keys said. "There's nothing better than this.''
The opening contrasted with last year's Grammys, where male acts dominated in nominations and the only woman competing for the top award, Lorde, didn't get a chance to perform onstage.
But this year, Gaga, Brandi Carlile and Kacey Musgraves won multiple Grammys.
Carlile won three honours in the Americana category and will compete for the three biggest awards during the live show: album, song and record of the year.
Gaga also won three, including best pop duo/group performance, a win she shared with Bradley Cooper.
"Thank you so much. I got to thank God, thank you for looking out for me. Thank you for my family,'' she said. "I wish Bradley was here with my right now.''
Gaga, now a nine-time Grammy winner, won best pop solo performance for Joanne, while hit Shallow, from A Star is Born, was named best song written for visual media. The song is nominated for an Oscar and also won at the Golden Globes, Critics' Choice Movie Awards and the Satellite Awards.
Women have a strong presence in the top categories. Five of the eight album-of-the-year nominees are women, including Carlile's By the Way, I Forgive You, Janelle Monae's Dirty Computer, Cardi B's Invasion of Privacy, Musgraves' Golden Hour, and H.E.R.'s self-titled album are also in contention.
Six of the best-new-artist nominees are women, including H.E.R., Chloe x Halle, Margo Price, Dua Lipa, Bebe Rexha and Jorja Smith.
Ariana Grande won her first Grammy in the same week that she publicly blasted Grammys producer Ken Ehrlich and accused him of lying about why she was no longer performing at the show.
"I know i'm not there tonight (trust, i tried and still truly wished it had worked out tbh) and i know i said i try not to put too much weight into these things .... but (expletive) ....... this is wild and beautiful. thank you so much,'' she tweeted after learning about her win.
Several big stars are not attending the Grammys, including Grande, Taylor Swift, Kendrick Lamar, the top nominee with eight, and Drake, nominated for seven awards.
Camila Cabello kicked off the show with a performance featuring J Balvin, Ricky Martin and Young Thug.