Few Iraqis, desperately trying to survive amid mounting violence and sectarian killings, would quarrel with Tony Blair’s assertion in Baghdad yesterday that the task of the international community was to ensure that democracy was not defeated by terrorism. Nor would Palestinians, facing the prospect of civil war between rival factions, disagree with his insistence that resolving the conflicts in Gaza and resuming peace talks with Israel must be priorities if this will unlock foreign aid and reduce regional tensions. The Prime Minister’s difficulty is that the turmoil in both areas is now so intense that few will heed what he says, or indeed even notice his visit.

Mr Blair rightly believes that Iraq and Palestine are two of the world’s most dangerous conflicts. He also believes that, with ten years of experience in the Middle East, he has the knowledge, authority and determination to use his last months in office to reverse the downward spiral and play a catalytic role in the search for peace. It is not simply his legacy on his mind (though anything that would improve the situation in Iraq would alter the perception of his premiership); it is his conviction that extremism, especially when yoked to religious fanaticism, is the greatest threat now to global peace and also to Western multicultural societies.

In both Iraq and Palestine, however, the issues have become more intractable and the violence more deadly. Mr Blair, rightly, rules out any quick withdrawal. “Don't be under any doubt at all. British troops will remain until the job is done,” he said, defying not only the cut-and-run lobby at home, but also those Americans who believe the Baker report should persuade President Bush to start pulling out. Both leaders have made their rejection of such counsel clear in the past two weeks. Beyond that, however, there was little that Mr Blair could do yesterday to shore up the fragile authority of the Iraqi Government and of Nouri al-Maliki, its Prime Minister.

Where he believes he can play a more powerful role is in persuading Fatah and Hamas to set aside their differences and resume the search for a settlement with Israel. He has long been convinced that Israel can be persuaded — given American engagement and support — to offer the Palestinians enough to get talks going again. Hopes were briefly raised last month that Ehud Olmert, the Israeli Prime Minister, was now ready to take political risks. But Mr Blair has underestimated the ideological enmity between Fatah and Hamas, between those ready to negotiate and those sworn to carry on the armed struggle. That enmity has fatally delayed the formation of a Palestinian government of national unity, the only likely hope that a formula could be found implying sufficient recognition of Israel to unlock the funds witheld by foreign donors.

President Mahmoud Abbas has now decided to force the issue with new elections. It is a dangerous gamble. Furious Hamas supporters have already taken to the streets and called for a boycott of any vote. Instead of new authority for the President, the result could be a slide into anarchy. Mr Blair’s diplomatic skills and determination to focus international attention may make little difference. There is little the outside world can do until Hamas, in particular, resolves its internal contradictions. Does it want peace and prosperity or conflict and chaos? Mr Blair is right to underline the dangers of letting things fester. He would also be right to see the limitations of any proposals put forward in his name alone.