"Recourse to military action is not going to help resolve the question of security on our borders," he said.
"There must be other ways to settle this problem because it's our problem too."
The Turkish government wants an incursion to flush out suspected rear bases of the Kurdistan Workers' Party, or PKK.
Erdogan said on Tuesday that all measures, including military ones, would be considered in the fight against the PKK.
Turkey says PKK fighters used bases in northern Iraq to launch a renewed offensive inside Turkey in which 15 soldiers died over the weekend.
It accuses the Iraqi Kurds of tolerating or supporting the PKK, which the regional government denies.
But Abdallah reiterated the regional government's official position that "we do not allow groups hostile to any of our neighbours to use Kurdistan to launch operations".
Hoda Abdel-Hamid, Al Jazeera's correspondent in Irbil, an Iraqi city about 300km from the Turkish border, said: "People are quite sceptical that Turkey would carry out a full-scale incursion these days."
She said: "They see that there is a lot of pressure from Baghdad and from the neighbouring countries to try to keep this part of Iraq - the only stable part of Iraq - as stable as possible.
"They expect a lot of international pressure on Turkey not to go ahead with this large-scale incursion."
Ilnur Cevik, the editor and chief columnist of Turkey's New Anatolian newspaper, agreed that Turkey would come under international pressure not to carry out an incursion.
"You can start a military incursion, but you cannot stay there because the United States will put up pressure and the European Union - which Turkey wants to join - will put up pressure ... despite the fact they feel that Turkey has a legitimate cause in fighting the PKK."
He told Al Jazeera: "The areas that we're talking about - deep inside the Iraqi Kurdish mountains where the PKK is holed up - mean you have to go 60km inside Kurdish territories. This is not the legitimate 'hot pursuit' that is allowed for Turkey by international law, it is an occupation."
"Turkey has warned of damage to bilateral ties and military co-operation if congress passes the measure"
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Turkey and Iraq signed an accord last month to combat the PKK, but failed to agree on a "hot pursuit" clause, requested by Turkey, to allow Turkish troops to pursue fighters across the countries' shared border if the need arose.
On Thursday, Javier Solana, the EU's foreign policy chief, urged Turkey not to launch military operations into northern Iraq, saying it would "complicate" the security situation in the country.
"The question of security continues to be a fundamental issue to the stability of Iraq," Solana said.
"Any possibility of complicating even more the security situation in Iraq is something that should not be welcomed. That is the lesson we pass to our Turkish friends."
Earlier on Wednesday, Washington again warned Ankara against unilateral action in northern Iraq.
Relations between Turkey and the US have already come under strain after US politicians voted to pass a bill labelling the 1915 massacre of Armenians by Ottoman Turks as genocide.
Turkey has called the resolution irresponsible and warned it could cause "serious troubles" to relations between the two countries.