The US cannot possibly accept the offer. It is a classic challenge, with a well-known sting — do you risk supplying weapons if they might simply arm one side of a civil war? In Iraq’s case the risk is so great that the answer must be no.

You can understand al-Maliki’s motives — above all, that the tough talk played well at home. The visit by Condoleezza Rice, Secretary of State, had been humiliating, with its warnings that the Iraqi Government was living on “borrowed time”.

The musings by President Bush seem almost to have been worse, particularly his acknowledgement that he had made “mistakes” in Iraq. “Shut up” was al-Maliki’s message back to him, put almost as bluntly as that. Insurgents took only encouragement from that phrase, he said, reading “failure” from the word “mistakes”.

Nor are Iraqis blind to the four separate resolutions introduced to Congress that may curtail Bush’s ability to deploy the “surge” of 21,500 extra troops that he has announced.

So al-Maliki’s challenge can be read as an opening offer, if you like, probing the weaknesses of his ally-turned-antagonist. “If we succeed in implementing the agreement between us to speed up the equipping and providing weapons to our military forces, I think that within three to six months our need for American troops will dramatically go down”. Or, as The Times front page headline yesterday put it bluntly: “Give us guns — and troops can go” .

The US cannot accept this offer — which forms no part of Bush’s “surge” plan — because it cannot trust al-Maliki to use those weapons in the pursuit of goals it shares. Specifically, it cannot trust him to prevent the arms being used for the suppression and persecution of the Sunnis, previously Iraq’s bureaucratic elite, making up a fifth of the population.

It may be, as his officials maintain, that he has every intention of dealing with the Shia militias — particularly those led by Moqtada al-Sadr. His philosophy, they suggest, is to crack down on the Sunni insurgency, in order to be able to tell Shias that they no longer have need of their own militias. He has no desire to have his government owe its authority and character to a wild, armed rabble in the streets. But nor, at the moment, can he get rid of it.

That does not, however, offer any reassurance to Sunnis. If the US were to supply al-Maliki with guns, they would very likely be used against Sunnis in what you might as well call a civil war. It would take Iraq even further from the US’s original hope that it would be a country encompassing Sunnis, Shias and Kurds, run by a representative government.

The US has chastised itself endlessly for the early decision to disband Saddam Hussein’s army, predominantly Sunni, although more mixed than many other branches of the regime. Perhaps it berates itself too much. It is hard to imagine that the original army would have held together under the sectarian strains of the past year.

Yes, the decision left many men unemployed, and armed. But even worse would be now to arm government-backed forces with the latest weapons —but with no control over the use to which it put them. Even if al-Maliki’s request is no more than an opening offer, the US should make clear that its answer is no.

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