On the level of public rhetoric, the stakes in yesterday’s meeting between President Bush and Recep Erdogan, the Turkish Prime Minister, could hardly have been higher: failure to agree on a workable plan to rein in the guerrillas of the PKK, or Kurdistan Workers’ Party, would put at risk a 56-year-old military alliance between the US and Turkey, the stability of northern Iraq and the integrity of Iraq itself. Success could consign the current crisis on the Turkish-Iraqi border to footnote status in the larger history of the region. Yet success already looks more plausible than many dared hope two weeks ago, when burning Turkish anger over PKK murders, and massed Turkish troops on Iraq’s northern border, appeared to make conflict all but inevitable.

Turkey and the PKK have since pulled back from the brink. The best evidence was the release on Sunday of eight Turkish soldiers kidnapped by the PKK. Turkish parliamentarians and Iraqi Kurdish officials were involved, but the pressure for a significant gesture came from the US and Mr Erdogan himself, who deserves praise for his forbearance and diplomacy.

The groundwork for last night’s hastily arranged summit was laid by Condoleezza Rice, the US Secretary of State. In Istanbul last week she affirmed the official US position that the PKK was a terrorist organisation, went further by calling it a “common enemy” and acknowledged that rooting out the threat it poses to Turkey would take persistence and commitment. Until now, commitment is precisely what Turkey believes has been missing from Washington’s approach to the Kurdish question, since Mr Bush’s assurances in 2003 of robust action against the PKK have necessarily been subordinated to fighting insurgencies to the south.

Northern Iraq’s elected Kurdish leadership has also, unsurprisingly, been slow to act against extremists encamped on territory that it nominally controls. The result has been a breathing space that the PKK has exploited without compunction or concern for the long-term wellbeing of the moderate Kurdish majority.

Its recent return to violence has left 30 Turkish soldiers dead and eight kidnapped in two ambushes on Turkish soil, enraging Turkish public opinion and bringing clamorous demands for a full-scale ground offensive in northern Iraq.

Such an offensive must be prevented at all costs. Mr Bush met Mr Erdogan at a time of measurable progress in central Iraq, progress that much of the world is choosing to ignore, but progress that would be compromised by a conflict in the north. But if the goal is clear, how to achieve it has been less obvious because of the northern Iraqi leadership’s reluctance, under the Prime Minster Nechirvan Barzani, to co-operate in shutting down PKK camps in the Kandil Mountains.

Thankfully there are signs of a reality check in Mr Barzani’s administration. He has issued a statement condemning the PKK for killings that had “no place in the modern civilised world”, and Iraqi Kurds hosted the secret talks that led to Sunday’s hostage release. As the most obvious beneficiaries of the ending of Saddam Hussein’s misrule, it was the least they could do. Iraq’s moderate Kurds must continue to accept their responsibility to act against the extremists operating from their territory.