More than 100 Turkish troops and Kurdish separatists have been killed in northern Iraq in three days of clashes since the Turkish Army crossed the border to attack PKK strongholds. The fighting is getting worse. Yesterday the PKK claimed to have shot down a Turkish helicopter, and its commanders in Iraq called on Kurds in Turkish cities to join in the fight. Meanwhile, Moqtada al-Sadr, the Iraqi Shia militia leader, demanded an immediate Turkish withdrawal and said he held the Iraqi Government and US forces responsible for the worsening situation on the borders.

The Turkish incursion is the first full-scale military operation in northern Iraq since the fall of Saddam Hussein. It comes after months of rising tensions, and despite urgent pleas from Washington for restraint. The clashes put America in an unenviable position. Turkey is a Nato member, an important military partner and a crucial factor in regional stability. The US has expressed understanding of its determination to root out terrorist sanctuaries across the border. But any invasion could destabilise northern Iraq, stir fierce anti-American anger among Kurds who have been largely supportive of the coalition forces and jeopardise the fragile coalition in Baghdad.

Recep Tayyip Erdogan, the Turkish Prime Minister, is equally constrained. For months he has faced down demands by Turkey's military Establishment for an invasion to crush the exiled PKK leadership and to thwart any attempt to establish an autonomous Kurdish government in northern Iraq. The Turkish army is deeply suspicious of Mr Erdogan, and last year came close to threatening a coup over the election of an Islamist president. Mr Erdogan was able to avoid intervention last year only because America promised swift action to curb the PKK in Iraq. But the army, which regards itself as the guardian of the Atatürk secular legacy, would not hesitate to move against Mr Erdogan if it believes he is weak in dealing with the PKK, whose terrorism has cost well over 40,000 lives in eastern Turkey.

The onus now lies on Baghdad to satisfy Turkish demands. However tempting it may be for Iraqi Kurds to give moral and military support to kinsmen in Turkey, it would also be disastrous. The PKK is a vicious terrorist organisation, and Iraq's Kurds, including the country's President, Jalal Talabani, must not only distance themselves from the PKK but also halt its cross-border operations and deny the terrorists haven in Iraqi territory. Turkey should show restraint, and limit its operations to hot pursuit. But Ankara is sceptical of Kurdish promises, made last year at American prompting, that were soon flouted as the PKK resumed hit-and-run operations in eastern Turkey. It is unlikely that renewed pleadings by Washington or Baghdad will have much influence over the Turkish general staff.

In its own interests, however, Turkey should be wary of escalation. It has long seen an autonomous Kurdistan as a threat to its national unity, fearing that the example would tug at the loyalties of Turkey's 20 million Kurds. The greater danger would surely be full-scale fighting on its border and the break-up of Iraq, which Turkish intervention and occupation would hasten. The Erdogan Government has gone farther than its predecessors in satisfying Turkish Kurds' aspirations. It should now pull back before all hopes of an historic reconciliation are jeopardised