A top EU official has urged France not to push ahead with a bill which he says could sour relations between the EU and aspiring member Turkey.
Protesters in Istanbul demanded that France drop the bill
French MPs are due to discuss the bill - which would make it a crime to deny that Turkey perpetrated a genocide against Armenians - on Thursday.
Turkey's foreign minister threatened economic sanctions against France if the bill succeeds.
EU enlargement commissioner Olli Rehn said the bill was "counterproductive".
Mr Rehn warned that the adoption of the draft law would have very severe consequences for discussion of the Armenian question, saying "instead of opening, it will lock the debate in Turkey".
He said nothing was achieved by an ultimatum, and called instead for an open dialogue in Turkey itself, and between Turkey and neighbouring Armenia.
The two countries have a common border, but no diplomatic relations.
Armenians say the Ottoman Turks killed as many as 1.5 million Armenians in a planned genocide in 1915, during World War I.
The Turkish government strongly denies the allegations of genocide, saying many Armenians and Turks died in a conflict raging at that time.
Turkish activists protested outside the French consulate in Istanbul on Sunday, while Turkish Prime Minister Recep Tayyip Erdogan declared the issue was "none of France's business".
Arguments have raged for decades about the Armenian deaths
Turkish Foreign Minister Abdullah Gul warned France could be barred from business projects in Turkey if the bill succeeded. "The French will lose Turkey," he said.
Mr Rehn made clear that recognition of the killings as genocide was not a condition for EU entry.
However French Interior Minister Nicolas Sarkozy said he thought it should be.
He also told France Inter radio that Turkey must meet three conditions for the bill to be dropped, Reuters news agency reported.
He called for a bilateral commission between Armenia and Turkey to discuss their history; for Turkey to reopen its borders with Armenia; and for Ankara to allow discussion of the "genocide" within Turkey.
The bill could be supported by French politicians looking to curry favour with France's large Armenian community, says the BBC's Oana Lungescu in Brussels.
But Mr Sarkozy - who has opposed the idea of Turkey's accession to the EU - has also been accused of trying to stir up anti-Turkish sentiment just as the EU is considering Ankara's progress on harmonisation.