The 20-year-old multi-Grammy winner made the comment midway through a crowd-pleasing set that kicked off with hit "Bury a Friend" and ended with "Bad Guy" and "Happier Than Ever".
Without directly referencing Friday's US Supreme Court ruling that overturned Roe v. Wade, which recognised women's constitutional right to abortion, Eilish said: "Today us a really dark day for women in the US"
"I'm just going to say that because I can't bear to think about it anymore in this moment."
She then dedicated "Your Power", a song about abusing power, to the subject.
Near the end of the set, she told the crowd that she was "so undeserving" of headlining.
"Thank you for letting me do it," she said. "I am so honoured to be here."
Eilish closed the first full day of music at the festival in southwest England, which returned for its 50th anniversary two years later than planned after the pandemic scuppered the 2020 and 2021 events.
Other acts on Friday included Wet Leg, Arlo Parks and Primal Scream.
Rachel Austin, a 43-year-old engagement officer from Lincoln in eastern England, said no one could prepare you for all the experiences on offer.
"It's just amazing, the pictures don't do it justice at all," she said.
'CONCENTRATION OF FREEDOM'
Friday was kicked off by rock band the Libertines on the Other stage, one level down from the Pyramid.
Before that Ukrainian President Volodymyr Zelensky appealed via videolink to the crowds, urging them to spread the truth about Russia's invasion.
"Glastonbury is the greatest concentration of freedom these days and I ask you to share this feeling with everyone whose freedom is under attack," he said in a recorded message that drew cheers.
Paul McCartney headlines on Saturday, a week after his 80th birthday, while Diana Ross and Kendrick Lamar top the bill on Sunday.