National Park Service spokesman Jerry Willis says the climber was at the base beneath the statue's foot Wednesday afternoon.
About 100 feet (30 meters) aboveground, the woman engaged in a four-hour standoff with police before two officers climbed up to the base and went over to her.
The Rise and Resist protesters acknowledged that the woman who climbed the statue participated in the unfurling of the banner but that her later actions were not part of their protest.
Rise and Resist, which reportedly formed after the 2016 election, said 40 people took part in the "banner action" and that Okoumou was one of them, though they were not aware of her plans to climb the statue later.
Willis says federal code of regulations prohibits hanging banners from the monument.
ICE refers to the Immigration and Customs Enforcement agency, whose recent reatment of families who have crossed illegally into the United States from Mexico provoked an global outcry. Police, standing on a ladder and a ledge nearby, tried to talk the climber into descending.
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Wearing a "Rise and Resist" T-shirt, the woman told authorities that she would only come down when parents were reunited with all migrant children separated from them by the Trump administration. At 5 p.m. the group posted a tweet to disavow any connection with the climber.
An official later identified the woman as Therese Okoumou.
Her climb spurred the evacuation of Liberty Island. Trump has said on Twitter that abolishing ICE will "never happen!"
Kaitlyn Schallhorn is a Reporter for Fox News.
A poem by Emma Lazarus inscribed on a bronze plaque, and located in the Statue of Liberty's museum, is seen by many as embodying the spirit of America, particularly in the lines: "Give me your exhausted, your poor, Your huddled masses yearning to breathe free".
The statue, a gift from France, was dedicated in 1886.