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Police investigated after a girl in the Hutt Valley area laid a complaint last week.
The man had allegedly created at least three fictitious profiles to send the messages, which Detective Kylee Cusin said had "a sexual undertone".
One of the profiles was under the false name of Nick Davis and featured a fake photo.
Ms Cusin said a 20-year-old Upper Hutt man had been arrested and would appear in court today. The charges had yet to be decided.
Ms Cusin said two teenagers had laid complaints and it was more than likely the offender had contacted others.
Police have called for any young women who have been inappropriately contacted by "Nick Davis" on Facebook to get in touch.
Wellington police spokesman Nick Bohm said police had identified a number of profiles allegedly belonging to the man.
"When you look at the number of people that those profiles are in contact with, there's a potential pool there that is quite concerning."
Meanwhile, girls using a popular Facebook page to sell and buy secondhand clothes have been warned about a "predator" profile.
The account named "Lisa Lee" has asked members of the Walk In Wardrobe group, used by more than 28,200 people, for pictures of them wearing underwear and see-through dresses.
Lisa Lee asked Sophie Burnside about her boyfriend before requesting a photograph of her in a G-string.
"It was really creepy ... you just have to be so careful with who you're dealing with on the internet because at the end of the day, you never really know who's at the other end of it."
Ms Burnside, 23, of Auckland, first encountered Lisa Lee after she posted a picture of a dress that she was trying to sell in the group late last year. But Ms Burnside was alarmed when Lisa Lee messaged her asking for a picture of her wearing the dress in heels.
When she didn't respond, Lisa Lee then contacted her again asking her if she got the first request and then messaged her through Facebook.
Netsafe's chief technology officer, Sean Lyons, said they had received a number of complaints about people making inappropriate contact through trading sites, including Trade Me, though none were from Walk In Wardrobe.
"When we choose to interact in a very public place, I guess we have to be prepared that as much as we like to think that we know and trust the people around us, there will be parts of our society that may want to contact us and we're not going to like what they say. People need to be mindful of that."
- Matthew Backhouse of APNZ and Amelia Wade of the New Zealand Herald