The pop star shared a heartfelt moment with fans before performing her single "Delicate" - wearing a rainbow dress - which was dedicated to the LGBT+ community.
"It's very brave to be vulnerable about your feelings in any situation, but it's even more brave to be honest about your feelings and who you love when you know that it might be met with adversity from society," she told her audience.
"This month and every month I want to send my love and respect to everybody who has been brave enough to be honest about how they feel, to live their lives as they are, as they feel they should be, as they identify.
"This is a month where I think we need to celebrate how far we've come, but I think we also need to acknowledge how far we have left to go. I want to send my love and respect to everybody who hasn't felt comfortable enough to come out yet... and may you do that on your own time and may we end up with a world where everyone can live and love equally and no one has to be afraid to say how they feel," she continued.
"When it comes to feelings and when it comes to love and searching for someone to spend your whole life with... it's all just really, really delicate."
Fans shared their appreciation for the message on Twitter after Swift's show, posting footage and quotes from the speech on social media.
Swift's tour lands in the UK and Ireland later this week, beginning on 8 June in Manchester, where she will perform two shows at the Etihad Stadium, before travelling to Wembley Stadium in London for two nights, and then to Dublin, at Croke Park Stadium.
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