However the governor`s office of the Diyarbakir region denied that he had been the target of an assassination attempt or that the car was hit by gunfire.
Demirtas "survived the assassination attempt unharmed thanks to the bullet-proof vehicle (in which) he was riding," the HDP said on its official Twitter feed.
The pro-Kurdish Firat news agency said that neither Demirtas nor his guards had heard a shot being fired but noticed the bullet mark when getting out of the car at the end of the journey.
There was also no indication that any bullet or cartridge had been found at the scene.
In a statement, the governor`s office of Diyarbakir said the car had been examined by the authorities and a mark three centimetres (1.2 inches) in width and height had been found on the left side of the rear window.
But it said no sign had been found that this was caused by "any kind of firearm" and it had in fact been produced by a "collision with a very hard object".
The statement said that Demirtas had been given police protection throughout his stay in Diyarbakir and during this time "no kind of attack against him or against his vehicle has been realised".
The incident comes with tensions riding high in Turkey between the authorities and the Kurdish minority as the government presses a four-month offensive against the banned Kurdistan Workers Party (PKK).
One of Turkey`s most charismatic politicians, Demirtas has won supporters for the HDP outside its main Kurdish base and has become a major rival of President Recep Tayyip Erdogan.
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