The speedy fall of the Taliban must not obscure the size of the task ahead

The surrender of Kandahar is an important moment in the campaign against terrorism. The war against the Taliban regime has achieved its objective in less time than expected. It is a mere two months since the bombing began.

It is not, however, the occasion for triumphalism. Jack Straw, the Foreign Secretary, struck too upbeat a note yesterday – "a terrific day not just for the people of Afghanistan, but for the whole of the world". His excitement is understandable, given his surprise and delight at the apparent vindication of the coalition's strategy. But let us rewind briefly to the days of shock and horror after 11 September. At that stage, the Taliban regime was being asked to yield Osama bin Laden and his associates to face justice. When it failed to do so, the removal of the Taliban became a secondary objective of the campaign. That secondary aim has now been fulfilled, while progress towards the larger objective has been ambiguous.

Al-Qa'ida has been weakened, and Mr bin Laden is closer to being apprehended than he was, but the collateral damage to civilians from the bombing has inflicted collateral damage on the campaign against terrorism. Inevitably, civilians will be killed in any substantial military action, and this action was justified on its own terms. Even though the Bonn agreement may already be unravelling, and whatever friction up to and including renewed civil war there may be between rival warlords, the likelihood is that the welfare and morale of the Afghan people as a whole will be better under the new dispensation than the old. (Although that does critically depend on the West's continued commitment.)

The civilian casualties of the past two months have, however, compounded the very resentment of United States power that fuelled extremist Islamic terrorism in the first place. The iconography of B-52s raining death on a poor and avowedly Islamic nation might be calculated to inflame anti-American opinion in the Arab and Muslim worlds.

One reason why triumphalism about the fall of the Taliban should be eschewed is because the US and its allies have shown insufficient regret and sadness at the deaths of Afghan villagers. This has allowed the propagandists of Islamic nihilism to claim that the US cares about the deaths of civilians in New York but not in Afghanistan.

The other reason is because the principal objective of the campaign – to make the US, and other Western countries, safe from suicidal Islamic terrorism – is still a long way from being fulfilled. It is vital that the lessons of phase one of the campaign, now drawing to a close, be applied to phase two. If the US intends to pursue al-Qa'ida in the next phase to Sudan, Yemen and Somalia – albeit probably not Iraq – this will have to be handled with extreme sensitivity.

The US must be brought to realise that it will only succeed in this campaign if it adheres scrupulously to the principles of international law; if it acts through the United Nations as much as possible, while being aware of the dangers of the UN being seen as an instrument of US policy; and if it attends to the legitimate causes of Muslim resentment.

Sadly, the renewed commitment of the US to a settlement of the differences between the Israelis and the Palestinians has been swept away in the predictable response to last weekend's suicide bombings in Jerusalem. George Bush the Isolationist was replaced on 11 September by Bush the Interventionist, but there are two kinds of interventionist foreign policy – one that emphasises military power to destroy and one that emphasises economic power to rebuild.

It is vital that in the next phase of the campaign the US and its allies understand, and act to soften, the common perception of America as the sole superpower, in control of the world's skies and prepared to bomb those who profess different values into submission.