The Democrat frontrunner also placed his hands on the girl’s shoulders for an extended period. Following a number of other similar displays, Mr Biden was nicknamed “creepy Joe” by President Trump. Before the 2016 election Trump was accused of inappropriate sexual behaviour by a number of women – claims he denies.
The incident took place in Texas on Tuesday.
Mr Biden was addressing an American Federation of Teachers town hall meeting.
Asked a question by the girl the top Democrat replied: “I tell you what hun, what I’m going to do, if you give me your address, I’m going to write you a longer answer and tell you the exact things I would do.
“I bet you’re as bright as you are good looking I tell you.”
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Mr Biden then asked the girl what her favourite subject is, to which she replied journalism.
Jokingly he responded: “I better be more circumspect in my answers!”
The Democratic candidate then took the girl by the hand and introduced her to journalists at the back of the room, while resting his hands on her shoulders.
Mr Biden said: “You see this Washington Post, New York Times, all these guys you ought to go back and talk to them okay.
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“The truth of the matter is the reason we are who we are is called a free press.”
From January 2009 to January 2017 Mr Biden served as Vice-President of the US, under President Barack Obama.
Prior to that he represented Delaware in the Senate for over 30 years.
Mr Biden is currently facing a strong primary challenge from the socialist Bernie Sanders.
During a TV interview last month the Democrat insisted that he “did not intend” to do anything inappropriate over claims of misconduct.
Mr Biden said: “I’m sorry this happened. But I’m not sorry in the sense that I did anything intentionally designed to do anything wrong or to be inappropriate.
“It was inappropriate that I didn’t understand and that I assumed.”