Aytac Baran, the leader of the Ihya-Der charity group, was shot dead by unknown gunmen outside his home in Diyarbakir, prompting a gunfight that left two others dead.
There was no information yet on the identities of the other victims. An earlier toll from the hospital sources had spoken of four people dead.
At least three journalists who were covering the clashes were injured, the Dogan press agency reported.
But the HDP, which made a strong showing in Sunday's general election, strongly condemned the attack in a statement and called for a thorough investigation.
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The party's leader Selahattin Demirtas called for calm. "A dirty scenario is at play. All parties should act with common sense," Demirtas wrote on Twitter.
Baran had been threatened by the outlawed Kurdistan Workers' Party (PKK) shortly before his assassination, his lawyer said in a statement quoted by Turkish media.
Police arrested three suspects for possession of weapons, Turkish media reported, citing the local governor's office.
Turkish media reports said two of the injured journalists were working for the DHA news agency and one for the IHA news agency.
DHA said the reporters were beaten up while covering the attack. Two were released from hospital but DHA reporter Canan Altuntas was still being treated.
Ihya-Der is linked to the Islamist group Huda-Par, known as the political arm of Turkish Hezbollah, a Kurdish Sunni Islamist militant organisation.
Violence frequently breaks out between Huda-Par and HDP members, who are seen by critics as close to the PKK.
The violence came after three people were killed and dozens more wounded in an attack on an HDP rally in Diyarbakir last week, in the final days of the election campaign.