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Turkey on Thursday renewed its aerial campaign on Iraqi Kurdistan, striking PKK targets in the northern mountainous region in retaliation against the killing of a Turkish diplomat in the region.

The Turkish vice consul to Iraq's autonomous Kurdish Regional Government (KRG) was shot dead on Wednesday by gunmen in the local capital Erbil.

There was no claim of responsibility for the attack, which killed two other people, but regional media has pointed to the role of the Kurdistan Workers' Party (PKK), a Kurdish militia which Ankara considers a terrorist organisation.

The PKK was founded in Turkey, where the group remains active since launching an insurgency against the state in the 1980s, but is based in Iraqi Kurdistan's Qandil mountains, where its bases and militants are frequently subjected to Turkish aerial bombing.

Ankara has in recent weeks increased its operations against PKK targets in Iraqi Kurdistan as part of its Operation Claw, but Defence Minister Hulusi Akar said that strikes directed against the group on Thursday were connected to Wednesday's attack.

"Following the evil attack in Erbil, we have launched the most comprehensive air operation on Qandil and dealt a heavy blow to the [PKK] terror organisation," Akar said in a statement according to AFP.

Targets including weapons positions, shelters and caves were destroyed, the minister added.

"Our fight against terror will continue with increasing determination until the last terrorist is neutralised and the blood of our martyrs will be avenged," he added.

A spokesman for the PKK's armed branch on Wednesday denied the group was involved in the shooting, which took place in an upscale Turkish restaurant in Erbil.

The KRG on Thursday identified one of three gunmen involved in the attack as Mazlum Dag, a Turkish citizen from Diyarbakir, a majority-Kurdish city in Turkey's southeast.

None of the suspects have been apprehended and a police search continues, with the KRG asking locals to "help turn in" Dag, according to Turkey's state news agency Anadolu.

The Kurdistan Democratic Party (KDP), which now leads the KRG, maintains close political and trade relations with Turkey.

While the PKK maintains bases in Iraqi Kurdistan, the militant group and the KDP are longtime rivals.