"We are not on the eve of a war," he told the National Press Club in Washington.
"We have made a decision on an operation. I want to stress once again that what we will do is an operation."
In response to what it sees as foot-dragging by Iraq and a lack of pressure from the US, Turkey has mustered 100,000 troops on the border with Iraq and threatened to go after the PKK if nothing is done to rein them in.
Gul said Turkey wants Iraq's stability more than anything.
"But stability does not just include Baghdad. Terrorists in northern Iraq are also a threat," he said.
"At the same time they are carrying out terrorist actions in Turkey as well. Turkey's aim is to end this terrorist organisation."
Bush has offered to share intelligence on Kurdish separatist fighters in northern Iraq with the Turkish government.
But the US is against Turkey sending thousands of troops across the border, fearing it could destabilise northern Iraq and cause a bigger regional crisis. It has not opposed limited military strikes.
Turkey is a crucial ally for Washington, which uses Incirlik air base to provide logistical support for its forces in Iraq.
Before meeting Bush, Erdogan had demanded Washington take "solid steps" against the Kurdistan Workers' Party (PKK).
After the meeting, Bush said: "The PKK is a terrorist organisation. They are an enemy of Turkey, they are an enemy of Iraq and they are an enemy of the United States.
"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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"In order to chase down people who murder people, you need good intelligence.
"We talked about the need for our militaries to stay in constant contact."
Bush also said that Erdogan had strongly urged the US to work with Iraqi leaders to cut off funding to the Kurdish fighters.
Al Jazeera's Hoda Abdel Hamid, reporting from Istanbul, said it would have been impossible for the US to agree to Erdogan's demands that all PKK bases be shut down and the group's leaders handed over to Ankara.
"The US has very limited resources at this stage in Iraq, and it certainly doesn't have the resources to pull out from the other troubled areas and put them in the northern mountains," she said.
Ankara has come under increased public pressure to act against the PKK after about 40 Turks, mostly troops, were killed in a series of attacks.
Meanwhile, Hoshiyar Zebari, Iraq's foreign minister, has said Baghdad has taken "tangible and serious measures" against the PKK.
He told Reuters news agency on Tuesday that a weekend meeting of Iraq's neighbours in Istanbul, talks between Erdogan and Bush and steps taken to curb the PKK's movements in northern Iraq had all contributed to easing heightened tensions.
He said: "A major military incursion into northern Iraq, and major is the key word, the chances of that are less.
"The Iraqi government has taken a number of tangible, demonstrable measures against the PKK. These measures will continue."