Mazloum Dag, 27, is "wanted" for Wednesday's murder of Turkish Vice Consul Osman and two Iraqis at a restaurant in the regional capital Arbil, the area's counterterrorism unit said.

A wanted notice released by the unit showed two photos of a black-haired young man with a close-cut beard, with one image apparently taken from CCTV footage.

"We call on all citizens to provide security services with information about this suspect as soon as possible," the counterterrorism unit said, adding that Dag is from Diyarbakir in Turkey.

It called the murder a "terrorist" act.

Turkey's Anadolu state news agency said the suspect is the brother of Dersim Dag, a member of Turkey's main pro-Kurdish party, the People's Democratic Party (HDP).

The HDP, the country's second largest opposition group, is regularly accused by President Recep Tayyip Erdogan of links to Turkey's outlawed separatist Kurdistan Workers' Party (PKK).

It "strongly" condemned the Arbil attack, calling it an "absolutely unacceptable provocation attempt".

The HDP also slammed the accusation that one of its deputies was "designated as a target because of his brother", without mentioning any names.

No group has claimed responsibility for the attack but Ankara on Thursday launched a "comprehensive air operation" against the PKK "terror organisation" in Iraqi Kurdistan's Qandil mountain area, defence minister Hulusi Akar said.

Turkey has been conducting a ground offensive and bombing campaign since May in the mountainous northern region to root out the PKK, which has waged an insurgency against the Turkish state since 1984.

Other air strikes Thursday night targeted "PKK bases and members" in the Makhmur area south of Iraq's northern city of Mosul, wounding two in a displacement camp, local sources to AFP.