Zebari did not outline what form Iraqi support for Turkey would take.
"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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"We will co-operate with the Turkish government, to solve the border problems and the terrorism that Turkey is facing through direct dialogue," he said.
Babacan told reporters in a joint news conference with Zebari that "politics, dialogue, diplomacy, culture and economy" were the measures to deal with the current conflict.
"We do not want to sacrifice our cultural and economic relations with Iraq for the sake of a terror organisation," he said, in reference to the PKK.
Babacan is also expected to meet Nuri al-Maliki, Iraq's prime minister, and Jalal Talabani, Iraq's president, during his visit.
Masrur Barzani, the head of security for the Kurdish regional government, told Al Jazeera the PKK problem cannot be solved by force and said his administration would not tolerate a Turkish incursion.
"We hope that Turkey does not export its own problems into our region," he said.
"But if we, for any reason become the target of a bigger, let's say, operation then we will do everything we can to defend ourselves."
Speaking in London on Tuesday, Recep Tayyip Erdogan, Turkey's prime minister, said Turkish forces were prepared for military operations against the PKK.
"Right now we are in a waiting stance but Iraq should know we can use the [parliamentary] mandate for a cross-border operation at any time," Erdogan told a joint news conference with Gordon Brown, Britain's prime minister.
Brown condemned the PKK attacks on Turkish forces and said he had offered the help of Britain's counter-terrorism unit to Ankara.
Kurdish fighters based in northern Iraq have denied reports of offering a ceasefire if Turkey abandons plans to launch cross-border raids against them.
A statement on a PKK website had said that the fighters were "ready for a ceasefire if the Turkish army stops attacking our positions, drops plans for an incursion and resorts to peace".
Al Jazeera's Hoda Abdel Hamid, reporting from northern Iraq, said PKK fighters based in the region had not confirmed the ceasefire offer.
"The leadership based here is denying that at this point of time a truce offer has been made," she said on Monday, underlining the confusion.
The PKK killed 17 Turkish troops in an attack early on Sunday in Hakkari province near the Iraq border.
Turkey's military said that 32 Kurdish fighters died in subsequent clashes, but also confirmed that eight of army soldiers were missing.
"Despite all search efforts, no contact has been established with eight missing personnel since shortly after the armed attack on the military unit," it said.
The apparent PKK ceasefire offer came just hours after Babacan said that all diplomatic efforts would be exhausted before troops were sent into northern Iraq.
Babacan said on Monday that if peaceful means failed, Ankara would "not hesitate" to use Turkish parliamentary authorisation which permits cross-border raids in pursuit of PKK fighters.
Meanwhile, George Bush, the US president, expressed his "deep concern" about Kurdish rebel attacks and told Abdullah Gul, the Turkish president, the US would continue to urge the Iraqis to take action against the PKK, the White House said.
Bush also spoke to al-Maliki, and the two agreed to work with Turkey to prevent the rebels from carrying out attacks from Iraqi soil.
Erdogan said late on Sunday that he had told Condoleezza Rice, the US secretary of state, during a telephone conversation that he expected "speedy steps from the US" to bring the PKK under control.
Iraq has urged restraint from Ankara and al-Maliki described the PKK raid as a "terrorist operation".
Abdel Qader al-Obeidi, the defence minister, appeared to suggest that the US military should take action against the PKK, saying that security in Iraq was the responsibility of the US-led coalition.
Residents of the main Kurdish cities of Arbil and Sulaiymaniah have said they fear the economic cost of any Turkish military action and some have started stockpiling food.