The NYPD is building a rope rescue system to help bring the woman down from the base, because officers don't believe she will come down on her own, a police source told CNN.
Willis says at least six people were taken into custody then.
So police placed her in custody, Willis said, noting that the woman was facing multiple federal charges including trespassing and disorderly conduct.
Park officials are reportedly negotiating with the woman to come down.
But members of the group said they had no idea she was going to scale the statue that day.
About 16 officers with the New York City Police Department took part in the risky rescue/apprehension effort, Officer Brian Glacken said in a news conference Wednesday evening. Around the same time, photos posted to social media appeared to show a single person climbing the statue near Lady Liberty's foot.
The group initially denied any connection to the climber, saying in a tweet, "The climber on the Statue of Liberty has no connection to our #abolishice action earlier today".
Okoumou allegedly "staged a unsafe stunt that alarmed the public and endangered her own life and the lives of the (New York Police Department) officers who responded to the scene", U.S. Attorney Geoffrey S. Berman said in a statement.
While the policy was abandoned, it is still unclear how and when some 2,000 migrant children will be reunited with their parents.
"Abolish ICE" has become a rallying cry at protests around the country and for some Democratic officeholders seeking to boost their progressive credentials.
Earlier in the afternoon, protesters with the Rise and Resist movement displayed a protest banner on the lower portion of the monument.
Police climbed after the woman, positioning ladders and negotiators in the hopes of talking her down.
The statue, a gift from France, was dedicated in 1886.
'An ABOLISH ICE banner was hung from the statue, and activists spelled out the same message on their shirts.
Inside LeBron James' Plan to Take Over Hollywood
The top markets for sales of LeBron's Lakers jersey were Los Angeles, New York, Oakland/San Francisco and Cleveland. LeBron James is to join the Los Angeles Lakers in a four-year deal worth $154m (£116m), his camp has announced.
China presses Europe for anti-U.S. alliance on trade
The name was leaked by news website Axios , which had earlier reported that the USA president wanted to leave the WTO. The tariff will take effect at the beginning of the day, but a specific time for China is unclear.
Another Heat Advisory Issued For Tuesday
Weekend Outlook: More typical afternoon scattered storms are expected on Saturday with highs in the lower 90s. Los Angeles is expected to reach 101 degrees on Friday while Las Vegas is forecast to reach 112 degrees.
Iconic LeBron James banner coming down in Cleveland
With James, the Lakers are now instantly a contender in the Western Conference, as they are getting the best player in the league. Chandler averaged 10.0 points and 5.4 rebounds last season for the Nuggets.
Extreme heat to stick around GTA for most of the week
However, daytime highs are still expected to be in the low 30s, with humidex values possibly reaching the low 40s. Toronto is also providing transit tokens for people experiencing homelessness to get to cool places.
UK police investigating 6 assault claims against Kevin Spacey
Spacey took to Twitter and claimed he didn't recall any such interaction, and apologised for his "inappropriate drunken behavior". Scotland Yard is investigating three new sexual assault allegations against Kevin Spacey , dating as far back as 1996.
Russian goalkeeper gives Spain the boot
Still, World Cup history was on Russia's side after its well-organized team survived two hours of barely having the ball. Akinfeev saved spot-kicks from Koke and Iago Aspas during a nerve-jangling finale at Moscow's Luzhniki Stadium .
Miles Teller to play Goose's son in 'Top Gun' sequel
The plot for the film will focus on the creation of drones and other new technology that is making human pilot's jobs obsolete. Skydance CEO David Ellison and Jerry Bruckheimer, producers of the original return to produce the sequel with Cruise.