Zebari said Turkey could instead carry out airstrikes on suspected PKK positions in northern Iraq.
"The Turkish decision does not serve Iraqi-Turkish relations, especially as it gives Turkish forces the authorisation to violate the sovereignty of another country."
Turkey's parliamentary voted on Wednesday to allow a military incursion in to Iraq to attack PKK fighters after a string of deadly attacks inside Turkey killed dozens of soldiers and civilians.
On Thursday, Ali Babacan, Turkey's foreign minister said Ankara wants to give diplomacy a chance, but insisted that it is determined to fight "terrorism" - a reference to the PKK.
Iraq's Kurdish administration also called on Thursday for direct negotiations with Ankara as thousands of worried Iraqi Kurds took to the streets to protest against the Turkish military threat.
"I think it is pretty difficult to say troops shouldn't [invade] when the Turkish soldiers are being killed, and their villages attacked"
Celtic, Karlstad, Sweden
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Zebari said that further dialogue was the only way to resolve the PKK problem.
"This party is not present with the approval of the Iraqi government or the government of the Kurdish region.
"The Iraqi government has asked them and other military groups to leave Iraq," Zebari said.
Asked if the government was giving the PKK a timetable to leave, Zebari said: "As soon as possible."
Al Jazeera's Hoda Abdel-Hamid said the foreign minister's comments are a "double blow" to the PKK because he is a Kurd.
She also said Zebari is echoing the lead taken by Nouri al-Maliki, the Iraqi prime minister, who dubbed the separatist group a "terrorist" operation.
Several thousand Iraqi Kurds took to the streets of their regional capital Arbil and the border town of Dohuk, holding the red, white and green Kurdistan flag - banned in Turkey.
"No no for the Turkish threat, yes yes for peace," shouted protesters in Arbil who carried banners written in Arabic, Kurdish and English.
|Thousands of protesters gathered in Arbil|
Protestors held up banners saying:" We condemn the Turkish threat," as they called on support from the international community.
They also held Kurdish flags and pictures of the late Mustafa Barzani, a Kurdish nationalist leader and the father of Massoud Barzani, Kurdistan's current president.
Barzani's government has implicitly denounced the actions of the separatist group, who have bases in their region, condemning "the killing of innocent people in Turkey," and saying violence did not solve any problems.