Stade Francais players began an open-ended strike last week, denouncing what they called a takeover in disguise, while the French federation and the Paris mayor also opposed the merger.
"I have decided to give this beautiful project up," Lorenzetti said in a statement.
"I have heard and understood the reservations... the social, human, sporting conditions are not met. Perhaps we were right too soon," he added.
"The future of Stade Francais will be written without us and I wish them the best."
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Stade Francais president Thomas Savare has previously said that he does not have the cash to keep the 14-times French champions afloat.
"I have heard the emotion, the surprise and the incomprehension of the fans, the players and members of our association," Savare said in a statement.
After Stade Francais's players went on strike on Tuesday, the French League (LNR) postponed games featuring the two Paris clubs this weekend, having met team representatives on Friday.
Another meeting was also scheduled for Monday, with LNR president Paul Goze and French federation boss Bernard Laporte also due to meet in the evening.
"We now have to build the future of this club in a collegial way," the head of the players' union and former Stade player Robins Tchale Watchou told Reuters.
(Reporting by Julien Pretot; Editing by Toby Davis)
