Foreign Minister Bernard Kouchner said he will travel to the Middle East in the coming days and would hold talks with Abbas, whose decision was seen in Paris as a new "threat to peace."
"I will press Mahmud Abbas to obstinately continue his work for peace, that is, for the creation of a Palestinian state," Kouchner said in Paris.
Israeli Foreign Minister Avigdor Lieberman dismissed Abbas' announcement as an empty threat, saying it was "nothing to get worked up about."
"He has resigned in the past during his tenure as Palestinian prime minister under chairman Yasser Arafat," said Lieberman, who is the first senior Israeli official to comment on Abbas' announcement.
Another official said Jerusalem had no intention of abandoning the efforts to jumpstart the peace talks "as soon as possible and without preconditions."
In Cairo, Arab League chief Amr Mussa urged Abbas to reconsider his decision and assured the beleaguered leader of his support, Egyptian state news agency MENA reported.