David Blaine -- I Didn't Cheat on My Fiancee ... 'Cause We're on a Break

David Blaine did NOT cheat on his fiancée when he got frisky with another girl in a club last night ... 'cause according to the magician, he and his woman are technically "on a break" ... a la Ross and Rachel.

Blaine was out at the 46 Lounge in New Jersey Thursday night ... when clubbers noticed David dancing verrry closely with some of the girls over the course of the night ... and putting his hands in some very interesting places.

Blaine is believed to be engaged to Alizee Guinochet -- a French model who happens to be the mother of his 1-year-old daughter ... but according to David's rep, the relationship is complicated.

"He and his fiancée have been on and off," David's rep tells TMZ .... adding, "But nevertheless he regrets his actions and is sorry if he caused her any embarrassment."

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