Three PKK female activists have been found dead with gunshot wounds to the head in the Kurdish Institute of Paris.
One of the women is said to be a co-founder of the militant Kurdish separatist movement, the PKK.
French Interior Minister Manuel Valls described the killings as “intolerable”.
The motive for the shootings is unclear. Some 40,000 people have died in the 25-year conflict between the Turkish state and the PKK.
However, Turkey has recently begun talks with the jailed PKK leader Abdullah Ocalan, with the aim of persuading the group to disarm.
“The scene [of the crime] could give rise to the idea that this was an execution, but the investigation will have to establish the exact circumstances of this incident,” a police source told French reporters.
A Kurdish news website in France identifies one of the women as Sakine Cansiz, a founder of the PKK, while another is said to be a representative of the Brussels-based National Congress of Kurdistan and the third is a young activist.
Manuel Valls said he would visit the scene of the shootings.
“These assassinations are intolerable, and I hope the inquiry will make rapid progress but let’s allow the investigators to do their work,” he told France-Info radio.
The Federation of Kurdish Associations in France has called for a demonstration in Paris.