The explosion, blamed by Defence Minister Fikri Isik on the outlawed Kurdistan Workers' Party (PKK), happened in the garden of the four-storey building in Elazig.
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Images on Turkish television showed severe damage to the building, with a large plume of black smoke rising from the headquarters.
Elazig is a conservative nationalist bastion and has been spared much of the violence that has struck the restive Kurdish dominated southeast.
Defence Minister Fikri Isik blamed the Kurdistan Workers' Party (PKK) for the attack during an interview with the state-run Anadolu news agency.
"We will thwart the PKK like we thwarted FETO," he said, referring to Fethullah Gulen who Ankara blames for the attempted coup last month.
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The PKK has kept up its assaults in recent weeks after the unsuccessful July 15 coup by rogue elements in the military aimed at unseating President Recep Tayyip Erdogan.
Eight people -- five police and three civilians -- were killed on Monday in a PKK car bomb attack on a police traffic control building on a highway leading southeast from Diyarbakir.
Two policemen and a civilian were killed in an attack on Wednesday night in Van, another city in the east.
Over 40,000 people have been killed since the PKK -- proscribed as a terrorist group by Turkey, the European Union and the United States -- first took up arms in 1984.
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