Turkey's ally Azerbaijan denounced as anti-democratic the French Senate's approval of a bill making it illegal to deny that the mass killings of Armenians during World War I were genocide.
"The Republic of Azerbaijan deplores the law adopted by the French Senate to criminalise the denial of the 'Armenian genocide' and expresses strong protest over this," the foreign ministry in Baku said in a statement.
The move was "against the principles of democracy, human rights, freedom of speech and expression", it said.
An official from the governing party said it had also undermined France's credibility as one of the members of the OSCE's Minsk Group, which is trying to help negotiate a solution to Azerbaijan's conflict with enemy Armenia over the disputed territory of Nagorny Karabakh.
"France's known actions have negated the remaining confidence in this group," said governing party executive secretary Ali Akhmedov, the Interfax news agency reported.
"In such a situation, the most honourable route would be if France removed itself from mediation as it has lost the moral right to fulfill this mission," he said.
Years of OSCE-mediated talks have so far failed to deliver a final peace deal in the conflict over Nagorny Karabakh, which was seized from Azerbaijan by Armenian separatists backed by Yerevan during a war in the 1990s.
Turkic-speaking, mainly Muslim Azerbaijan has the backing of Turkey in the conflict and has threatened to use force to reassert control if talks do not deliver results.
Like Ankara, Baku rejects the Armenian genocide allegations as false.