But that assertion depends on the US claim that there were few civilians left in Fallujah by the time the assault began last November. There is strong evidence to support the US position. But conflicting reports, inevitable in the circumstances, leave room for debate, and even more for rumour.

Even if the US is right on the legality, there is no question that it has inflicted a serious propaganda blow on itself. No matter the technical explanations of how useful the chemical is in flushing out insurgents from cellars. In using a weapon notorious in Vietnam, with effects on the human body straight from a science fiction film, it has given a gift to its enemies. It is now loudly accused of hypocrisy: justifying the war partly by Saddam Hussein’s use of chemical weapons, but then using particularly nasty ones itself.

Worse: the muddle of official denials, followed by an admission of use (in a limited sense), has fuelled those who disbelieve every American assertion.

The most directly applicable international law is Protocol III of the 1980 Convention on Conventional Weapons. Under this, the use of white phosphorus is prohibited as an incendiary weapon against civilian populations. It is also banned (with clear inspiration from Vietnam) in air attacks against military forces in civilian areas.

The US is not a signatory to Protocol III, although Britain and 80 other countries are. Defence Secretary John Reid said this week that British troops “do not use white phosphorus . . . for anything other than a smokescreen to protect our troops when in action”.

So the US has no problem arguing that it has broken no law to which it is a signatory. But it can also argue that it has not broken Protocol III — provided that its claim that civilians had left Fallujah before the attack started is right.

It strongly denies the claim by an Italian documentary that it used the weapon against civilians. It is true that it gave them clear warning over days, and an estimated 300,000 people did leave. But the US’s critics say that many remained.

The US is a signatory to the 1993 Chemical Weapons Convention, but denies that this covers white phosphorus.

The convention bans the use of any “toxic chemical” weapons that cause “death, harm or temporary incapacitation to humans or animals through their chemical action on life processes”. It says that the effect is incendiary, not chemical.

But even if it considers itself on firm legal ground, it has created a nightmare of public relations at the point when it is trying to court support in Europe and the Middle East.

Allegations of unusual weapons have been around since the assault. The US denied them, until internet bloggers unearthed personal accounts by the US military. On Tuesday Pentagon spokesman Lieutenant-Colonel Barry Venable said that the substance had been used as an “incendiary weapon against enemy combatants”, contradicting earlier statements by the London and Rome ambassadors, and the State Department website.

If there was anything that could make perceptions worse, it was the military slang of “shake and bake” attacks, phosphorus being the “bake” part.

It will take a lot of work by Karen Hughes, the President’s emissary, to improve the American image abroad, to make up for the incendiary effect on hearts and minds.

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