The document discloses for the first time the extent of private reservations within Tony Blair’s government about Washington’s approach.

It blows apart Blair’s public insistence that there are no differences between Britain and America over military tactics in Iraq.

Under the heading Problems, the memo says: “We should not underestimate the present difficulties . . . Heavy-handed US military tactics in Falluja and Najaf some weeks ago have fuelled both Sunni and Shi’ite opposition to the coalition, and lost us much public support inside Iraq.”

It adds: “The scandal of the treatment of detainees at Abu Ghraib (prison) has sapped the moral authority of the coalition, inside Iraq and internationally.”

The detailed memo, intended for senior ministers and top officials, talks of “the need to redouble our efforts to ensure a sensible and sensitive US approach to military operations”.

The memo acknowledges that Britain is struggling to get the Americans to adopt the more tactful approach that it wants and that there is a need to stop the United States doing anything “which would jeopardise our objectives”.

It also discloses that the Ministry of Defence (MoD) is considering two options for troop deployments to reinforce southern Iraq, both of which would involve extending the area patrolled by British soldiers.

Since the abuses of prisoners at the American-run Abu Ghraib jail in Baghdad came to light, Blair has been scrupulously careful not to criticise the Bush administration — although Jack Straw, the foreign secretary, has been less restrained.

The document, entitled Iraq: The Medium Term and dated May 19, was drawn up by the Iraq directorate in the Foreign Office. It was circulated to senior ministers and officials last week in the run-up to the June 30 deadline for handing over power to an Iraqi government.

While the six-page paper reveals candidly the government’s private misgivings about American tactics, it is accompanied by a one-page supplement with “public lines to take” by ministers. The official script instructs ministers to go no further than admit that “the security situation in Iraq is difficult”.

The disclosure will add to the pressure on Blair to voice the criticisms made in the document to President Bush both publicly and privately.

Last week Michael Howard, the Tory leader, criticised Blair’s “new doctrine” of not making public the private advice that he is giving the United States over Iraq.

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