The United States for the first time has expressed concern that Turkey is planning a longer stay than it promised, when 35,000 Turkish troops entered Iraq 10 days ago.
The Turkish media's portrayal of the invasion as an important military victory appears to tie Ankara's hands, should it wish to withdraw its forces. One Turkish commentator said: "The sense of national pride is higher than at any time since the invasion of Cyprus in 1974."
If these expectations are disappointed, the government may suffer from a popular backlash when the present euphoria peters out. According to the army's figures - and unlike previous offensives, it has not produced any dead bodies - Turkish soldiers have so far killed 199 guerrillas and captured 12.
The forces of the Kurdish Workers' Party (PKK) in Turkey and Iraq are thought by military specialists to number 10,000.
Turkey is playing down the warnings from Washington about the duration of the invasion, codenamed Operation Steel by the Turkish Army.
But, the government appears to be surprised by the extent of the international condemnation of its actions.
On Monday, the German Chancellor, Helmut Kohl, froze a $107m (£67m) military aid package, in protest against the invasion. At the same time, the US Secretary of State, Warren Christopher, said he had told Ankara of his concern about the length of the operation and violations of human rights.
The US has hitherto been more supportive of the offensive than its European allies, as it needs Turkish backing to maintain sanctions against Iraq.
But it may be concerned that the occupation of part of Kurdish territory by Turkey is discrediting the four-year-old US policy of supporting Kurdish autonomy in Iraq's three northern provinces through air power. The offensive also might give an excuse to Iran to launch its own invasion, in pursuit of Iranian Kurdish guerrillas with camps in Iraq.
While there is little public criticism, there is private scepticism in Turkey about the operation.
The Prime Minister, Tansu Ciller, has compared the army's success to the invasion of Cyprus and even to the heroic resistance of Turkish troops at the siege of Plevna by the Russians in 1878, although in the latter case, the Turks were defeated in the end.
Turkish commentators who are informed about the PKK say that the invasion is unlikely to do more than disrupt PKK plans to launch attacks this summer while it waits to see the outcome of the situation in northern Iraq. They add that recent clashes between the army and the PKK in Turkey, in any case, took place far from the Iraqi border.
"Any losses can be replaced by Kurds that the PKK has already recruited in Europe," one specialist on the movement said. "They also have not activated their units in Turkish cities, where the Kurds are a large minority."
The army says that it has seized 652 Kalashnikov automatic rifles, 42 rocket launchers and 16 mortars. But many of those on display look obsolete. In Kurdistan, where everybody carries a gun, it is easy to buy new weapons.
Inside Iraqi Kurdistan, the UN High Commission for Refugees is planning a second convoy to evacuate 1,400 Turkish Kurd refugees from the town of Zakho. This is in addition to 3,000 who were evacuated from the Turkish occupation zone on Sunday. A group of 177 men, women and children pushed their way into the UN compound in the town yesterday demanding to be taken to safety. They parked a minibus and 10 trucks, one of them full of sheep, and set up camp on a football pitch on a promise the United Nations would escort them to safety by tomorrow along with other refugees.