The 32-year-old pop star attempted to end her longtime feud with Swift in an interview Saturday with Ariana Huffington on The Thrive Global Podcast.
"I am ready to let it go," Perry told Huffington. "I forgive her and I'm sorry for anything I ever did, and I hope the same from her. I think it's actually like, I think it's time. There are bigger fish to fry, and there are real problems in the world.
"I love her, and I want the best for her," she added.
"I think she's a fantastic songwriter, and I think that, you know, if we, both her and I, can be representatives of strong women that come together despite their differences, I think the whole world is going to go like, 'Yeah, well we can do this.'"
Perry confirmed on "Carpool Karaoke" with James Corden in May that her beef with Swift began over backup dancers.
She explained in an interview with NME last week that she called out Swift to share her "side of the story."
"I wish that I could turn the cheek every single time, but I'm also not a pushover, you know? Especially when someone tries to assassinate my character with little girls. That's so messed up!" the star said.
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Perry told Huffington she hopes she and Swift can put their conflict behind them even if they still don't necessarily agree.
She accentuated her point by breaking out into the song "Let It Go" from the Disney movie "Frozen."
"I just really truly want to come together in a place of love and forgiveness and understanding and compassion," the singer said.
"There's a lot of other things out there in the world that people need to be focused on, and I truly, like, God bless her on her journey. God bless her. Honestly," she added.
Perry's apology came one day after the release of her new album, Witness. The record includes the singles "Chained to the Rhythm" and "Swish Swish" -- the latter of which is believed to be about Swift.
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