The nuclear deal will curb Iran's nuclear programme and end most economic sanctions imposed on country.
"Talks will not be extended beyond Monday, but there is still work to do," Iranian foreign minister Javad Zarif was quoted as saying.
US Secretary of State John Kerry also warned that "major issues" remained, but said he was hopeful.
Fabius, who cancelled a trip to Africa to stay at the talks, said: "I hope we are finally entering the final phase of these marathon negotiations. I believe it."
Iran reached a framework nuclear deal with the P5+1 on April 2. Negotiators are now seeking a final agreement that would restrict Iran's nuclear program in exchange for sanctions relief.
China, France, Russia, the United Kingdom, and the United States, plus Germany are called P5+1.