Three Kurdish women activists - including a co-founder of the militant nationalist PKK - have been found dead with gunshot wounds in a Kurdish information centre in Paris.
The bodies of Sakine Cansiz and two others were found on Thursday.
France and Turkey both condemned the killings.
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.
French President Francois Hollande described the killings as "horrible", while Interior Minister Manuel Valls said they were "surely an execution".
"Rest assured that French authorities are determined to get to the bottom of these intolerable acts," he said.
"I condemn this violence," Turkish government spokesman Bulent Arinc told reporters. "This is utterly wrong. I express my condolences."
The BBC's James Reynolds in Turkey says two rival theories have emerged about the killings.
The deputy chairman of the ruling party, Husein Celik, said that the killings appeared to be the result of an internal Kurdish feud.
The theory was later picked up by other officials and commentators in the Turkish media, who suggested that PKK factions opposed to the talks were to blame.
But Kurdish activists said the killings were carried out by forces in the Turkish state itself who wanted to derail the talks.
Our correspondent says that in Turkey many believe that there is a so-called "deep state" - a powerful nationalistic establishment which seeks to undermine the work of democratic governments and activists.
The three women were last seen inside the information centre on Wednesday afternoon. Later, a member of the Kurdish community tried to visit the centre but found the doors were locked.
Their bodies - all three bearing gunshot wounds - were found in the early hours on Thursday.
One of them was Sakine Cansiz, who was detained and tortured in Turkey in the 1980s, and was close to Ocalan.
A second woman has been named as Fidan Dogan, 32, who worked in the information centre. She was also the Paris representative of the Brussels-based Kurdistan National Congress.
The third, named as Leyla Soylemez, was a young activist.
Hundreds of members of the Kurdish community demonstrated outside the information centre as Mr Valls arrived.
Mr Valls said the French authorities were determined to "shed light on this act".
"In this neighbourhood, in this Kurdish information centre, in the 10th arrondissement [district] where many Kurds live, I also came to express my sympathy to the relatives and close friends of these three women," he said.
A representative of the Federation of Kurdish Assocations in France (Feyka), Leon Edart, told the French BFM news channel that there were no CCTV cameras in the office.
The PKK took up arms in 1984, and demands greater autonomy for Turkey's Kurds, who are thought to comprise up to 20% of the population.
It is regarded by Turkey, the US and European Union as a terrorist organisation, because of its attacks on Turkish security forces and civilians.
In 2012 it stepped up its attacks, leading to the fiercest fighting in decades, but violence has subsided during the winter.