Fabius, in Geneva for what is now a third day of intensive negotiations, said earlier in the day there was "no certainty" a deal could be reached and that Israel's "concerns" need to be taken into consideration.
Hossein Naqavi Hosseini, spokesman of the parliamentary foreign affairs committee, said "the behaviour of the French representative in the nuclear talks shows that France is trying to blackmail" Iran.
"While the French people want better ties between Tehran and Paris, unfortunately the French government prefers the will of Zionist regime," said Naqavi Hosseini.
Esmaeel Kosari, a fellow conservative and member of the committee, expressed regret that Fabius's comments "express the positions of the Zionist (Israeli) regime, which prompts us to eye the talks with pessimism."
And state news agency IRNA accused Fabius of "hindering" a deal between Iran and the so-called P5+1 group — Britain, China, France, Russia, the United States and Germany.
Fabius told France Inter radio that "there is an initial draft that we do not accept… As we speak, I have no certainty that we can finish up."
"There are some points on which we are not satisfied," he said, citing the "extremely prolific" Arak nuclear reactor and the question of uranium enrichment.
Fabius also expressed concerns over Iran's stockpile of 20 percent enriched uranium.
Israeli Prime Minister Benjamin Netanyahu warned that the United States was offering Iran the "deal of the century," saying the proposed agreement was "very bad."
Israel also vowed not to be bound by any international agreement and reserved the right to do whatever is necessary to defend itself — a clear allusion to a pre-emptive military strike.
Iranian Foreign Minister Mohammad Javad Zarif said there were divisions among the world powers attempting to negotiate a landmark deal with Tehran over its nuclear programme.
"We have reached an agreement on some questions, but on others there are still disagreements…. There are differences of opinion within the P5+1 group," he was quoted as saying by Iranian news agency ISNA.