The statement came a day after PKK rebels started withdrawing to bases in the Iraqi mountains. It was not clear if the Baghdad government would try to stop the process, expected to take several months.
Deniz confirmed that the PKK's withdrawal process began on Wednesday. He gave no details on the numbers of fighters that had begun to retreat or if any had crossed into Iraq.
Iraqi and Turkish officials were not immediately available for comment.
PKK has sought greater autonomy and more rights for Turkey's Kurds. The armed conflict between the two sides began in 1984.
In addition to the dispute over developing oil resources, the Kurds and the central government in Baghdad have been in a long-running dispute over lands claimed by the Kurds, power-sharing and rights to develop other natural resources.
Along with Sunni Arabs, the Kurds accuse Iraq's Shiite Prime Minister, Nouri al-Maliki, of amassing power in his hands and marginalizing political opponents.
Relations between Iraq and Turkey have been strained since December, when fugitive Sunni Vice President Tariq al-Hashemi took refuge in Turkey following accusations by Shiite-led government that he was running death squads. Turkish officials rejected Baghdad's request to hand over al-Hashemi, who was tried and convicted in absentia.
Turkish support for Sunni-led anti-government protests and a unilateral energy deal with Iraqi Kurds has added tension to relations between Baghdad and Ankara.
Associated Press writer Suzan Frazer in Ankara, Turkey contributed to this report.