46-year-old Michael Gordon is charged with kidnapping, assault and acting in a manner to injure a child.
The incident happened Saturday afternoon inside an apartment building on Broad Street in the St. George section.
Police say the girl was on the third floor in the hallway with her friends.
They exchanged some words with the suspect before he grabbed the girl around the waist and pulled her into the stairwell, investigators said.
But she was able to fight him off and was not hurt. The man took off on foot.
Police say he and the victim did not know each other.
According to the NYPD, Gordon has a long arrest record for crimes including drugs.
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