Abbas had been planning to deliver the threat in a letter to Israel. But, according to a copy of the letter obtained Thursday by The Associated Press, the language has been dropped from the text.
The diplomats who provided the letter said Abbas scrapped the threat at the urging of President Barack Obama.
The diplomats spoke on condition of anonymity because the letter has not yet been sent.
Dismantling the Western-backed Palestinian Authority has always been considered a last-resort option for the Palestinians. The move would mean the end of peace efforts and force Israel to take responsibility for the well-being of several million Palestinians.