One witness told the Daily Star newspaper: "They were banging on the windows and managers were worried they would smash the glass."
Niall required a minder when he tried to take photographs in the iconic Times Square before he was told to return to the hotel.
Some female fans were hanging from lampposts in a bid to get closer to the 'What Makes You Beautiful' hitmakers, and New York road signs were also vandalized when the group arrived in the city.
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The band broke an audience record for an online radio performance after it attracted around 40,000 of their fans, six times more than Justin Bieber pulled in for a previous session.
One Direction's 'Up All Night' album recently topped the US iTunes charts and their performance on America's 'Today' show on Monday drew in crowds of 15,000 screaming fans as they sang hit songs at New York's Rockefeller Plaza.