A woman was arrested after staging a protest against President Donald Trump's separation of migrant families by climbing the Statue of Liberty and forcing its evacuation on Independence Day.

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.

"She resisted at the beginning. She would not come down by voice command," said National Park Service spokesman Jerry Willis.

Police placed her in custody, Mr Willis said, noting that the woman was facing multiple federal charges including trespassing and disorderly conduct.

After nearly four hours on the statue, the woman finally accompanied police down off the monument, tethered to them by wires.

The woman, who has not yet been identified, at one point walked from one side to the other beneath the statue's sandal.

New York Police assisted US Park Police to remove her from the statue, which was once seen as a welcome sign for immigrants coming to the US.

Local media first reported that the woman was among demonstrators opposed to Mr Trump's immigration policy who protested at the site earlier in the day.

But Rise and Resist NYC, which organised the protest, said her protest on the statue was not part of its move.

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At least six people were arrested for hanging a banner around the base of the statue that read "Abolish ICE," referring to US Immigration and Customs Enforcement, the agency at the forefront of the immigration debate.

They too were facing misdemeanour federal charges, Mr Willis said.

Cruise operator Statue Cruises said it had to turn away more than 2,000 people waiting to take their tour to the famed statue.

Mr Trump has made cracking down on illegal immigration a cornerstone of his administration. 

As a result of the crackdown, distraught children were separated from their families and, according to widely broadcast pictures, held in chain-link enclosures.

His one-time "zero-tolerance" practice of separating migrant parents from their children at the Mexican border triggered international condemnation. 

While the policy was abandoned, it is still unclear how and when some 2,000 migrant children will be reunited with their parents.

Many trying to cross the US-Mexico frontier are destitute, fleeing gang violence and other turmoil in Central America.