Ankara is fighting a war against the Kurdish YPG militia, which it sees as an ally of the banned Kurdistan Workers’ Party (PKK).
The Turkish presidential spokesman swiftly rejected the French offer.
The spokesperson, Ibrahim Kalin said that countries should make it clear regarding their stance against “all types of terrorism”.
In another instance, Turkey said that five soldiers were killed and another seven were wounded in an attack by the PKK in the south-eastern province of Siirt.
The attack is being considered to be the deadliest one by the PKK for months and is being taken as a revenge for Turkey’s current offensive in northern Syria, said a reporter from Syria.
President Emmanuel Macron had arranged meetings with the members of the Kurdish-dominated Syrian Democratic Forces (SDF), which includes the YPG and expressed hopes for dialogue between Turkey and the militia.
His office said he had “paid tribute to the sacrifices and the determining role” of the SDF in the fight against the Islamic State (IS) group.
The SDF is considered to be a key US ally in the fight against IS and the Kurdish YPG forms a core part of it.
France and the US have provided the militia weapons and required training to support its battle against ISIS. The US also supports the YPG’s assertion that it has no direct organizational links to the PKK Party, which Turkey labels as a terror group.
The president said France would certainly support the “stabilization” location in the security zone in north-east Syria to stop IS regaining strength.
Kurdish officials said Mr Macron had committed himself to sending more military troops to the area but Paris declined to comment on that.
France has suffered a series of deadly terror attacks claimed by IS in recent years at home, including the Paris attacks which killed at least 130 people in 2015.
A week ago an IS sympathizer attacked and killed three people in a rampage in southern France, including a French police officer who died after swapping places with a hostage.
Mr Kalin replied on Twitter, reasserting the Turkish position that the PKK and YPG were trying to legitimize themselves under the SDF.
He wrote: “We reject any efforts to promote ‘dialogue’, ‘contact’ or ‘mediation’ between Turkey and those terrorist organizations.”
He said “friendly countries” should not “legitimize the structure of terror”
Earlier this month Turkey ousted Kurdish fighters from the Syrian-Kurdish city of Afrin located in Syria. Activists said 280 civilians had been killed, although this was denied by Ankara.
More than a quarter of a million civilians are said to have left the city.
Turkey has since then threatened to attack the SDF-controlled town of Manbij in Syria bordering Afrin, which was taken from IS in 2016 – and where the US has stationed troops.
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