The 20-year-old multi-Grammy winner made the comment midway through a crowd-pleasing set on the famed Pyramid stage 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 the 1973 Roe v Wade decision - which recognised women's constitutional right to abortion - Eilish said: "Today is 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 said.
She then dedicated Your Power, a song about abusing power, to the subject.
Near the end of the set, she told the crowd 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.
Friday was kicked off by rock band the Libertines on the Other stage, one level down from the Pyramid.
Before that, Ukrainian President Volodymyr Zelenskiy 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.
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