"The United States has given the order for the capture of the leadership of the PKK terror group," the state-run Anatolian news agency quoted General Ilker Basbug, second in command at Turkey's politically influential General Staff, as telling senior media executives.
Basbug also said on Tuesday that Turkey had the right to stage an incursion into Iraq against PKK fighters.
Ankara has repeatedly pressed the US to act against the PKK in Iraq. The Turkish military says about 3000 fighters are in the northern mountains in a region controlled by Iraqi Kurds.
"We expect Baghdad to show it cares for Turkey's security, just as we care for Iraq's security and stability," Foreign Ministry spokesman Namik Tan told reporters.
Tan added: "Turkey will naturally take the measures it deems necessary when it deems it necessary."
Tan's remarks came as Iraqi Interior Minister Bayan Solagh joined counterparts from Turkey and other neighbouring countries at a meeting in Istanbul to discuss regional security.
A US embassy spokesman said he could neither confirm nor deny the remarks, saying he could not comment on operational matters.
"Turkey will naturally take the measures it deems necessary when it deems it necessary"
Turkish foreign ministry
Before the US-led invasion of Iraq in 2003, when Kurdish-held northern Iraq was outside Baghdad's control, the Turkish army made incursions into the region allegedly to hunt down PKK fighters, with tacit US approval and ground support from the local Iraqi Kurds.
However, analysts say Washington, which like the European Union includes the PKK on its list of "terrorist groups", has had its hands full battling fighters opposed to US-led forces in Iraq and has been reluctant to open a new front against the PKK.
Turkey's General Staff says the rebels have crossed into Turkey more frequently and in large numbers in the past year and number nearly 2000 inside the country, carrying out attacks on what it says are military targets in the mainly Kurdish southeast.