Turkish military sources have denied that its troops crossed into northern Iraq on Friday night.
Iraq's Kurds fear the arrival of any Turkish troops
Earlier reports quoting both Foreign Minister Abdullah Gul and unnamed military sources had suggested that commandos crossed the border to prevent a flood of refugees.
Kurds in northern Iraq also told the Reuters news agency that no Turkish forces had arrived.
The denial comes amid fears that any incursion by Turkish trooops would raise tension with Iraqi Kurds and Turkey's Nato allies.
Turkish officials have in recent days repeated their determination to deploy the army in order to strengthen the security along the 300km-long border (about 190 miles).
But the US opposes such a move, fearing clashes between Turkish forces and Iraqi Kurdish factions and has repeated its objection to any unilateral move by the Turks into the area.
We do not see any need for Turkish incursions into northern Iraq
US Secretary of State Colin Powell
Turkey wants to prevents the Kurds forming a separate state. Iraqi Kurds say the presence of Turkish troops would threaten Iraq's territorial integrity.
The BBC's Jim Muir, who is in northern Iraq, says Iraqi Kurds fear a Turkish move would be directed against them rather than the Iraqi army.
Although the two main Kurdish factions are not threatening to attack the Turks, they have both said that the Kurdish people would not accept a Turkish presence and that sooner or later there would be trouble.
German Foreign Minister Joschka Fischer threatened to withdraw its crews from Nato Awacs surveillance planes patrolling Turkish airspace if Ankara orders an invasion of Iraq.
Aid package withdrawn
After a long debate, Turkey decided to open its airspace to US warplanes attacking Iraq on Friday.
Turkish Defence Minister Vecdi Gonul told reporters the airspace agreement with the US was "in Turkey's interests".
He announced the decision after talks with Prime Minister Recep Tayyip Erdogan and senior military and civilian officials.
Friday's agreement came after earlier talks between Turkey and US failed to resolve their differences.
Before the deal was announced, US Secretary of State Colin Powell had said: "At the moment we do not see any need for any Turkish incursions into northern Iraq."
The US originally asked Turkey to grant permission for 62,000 of its troops to use the country as a launch-pad for an attack on Iraq.
Turkey would have received a multi-billion-dollar compensation package in return, but US officials say the financial package has now been withdrawn.
Correspondents say that the airspace agreement allows an air bridge to be established to ferry special forces to a number of airfields in Kurdish-held northern Iraq.
This enables a northern front to be mounted against Iraqi Government forces.