President Obama is to put Gordon Brown under pressure to deploy more troops in Afghanistan after senior figures in his Administration declared Britain and other Nato allies needed to start "talking specifics" about what more they can contribute for the war effort.

After months of indecision about whether to extend the UK's military commitment beyond the current level of around 8,000 personnel, the Prime Minister faces a test of the alliance he forged with Mr Obama this week at the G20 summit when the caravan moves on to a meeting of Nato in Strasbourg this weekend.

Hillary Clinton, the US Secretary of State, said yesterday that although the Nato summit is not a pledging conference, "of course we'll be talking about how our allies can match their resources to the needs identified in the strategic review" of policy in Afghanistan that Mr Obama unveiled last week.

Asked by The Times if the Adminstration was pushing for more British troops, she replied that all America's allies in Afghanistan had been asked to conduct their own review so that they "take a hard look at what they believe is their highest and best contribution". She added: "We'll begin talking in specifics at the NATO summit in Strasbourg."

In a press conference last night where he hailed an "historic" achievement at the G20 summit, Mr Obama made pointed reference for the need for co-ordinated international action on a range of other issues including fighting terrorism and stabilising Afghanistan."

Mr Obama has so far been rebuffed by many allies, including those from Europe, who have said they are unwilling to follow his lead in committing more troops to the war. Advisers believe their most realistic hope is to secure additional funds for rebuilding Afghanistan and help with training the country's own security forces.

Disclosures that Hamid Karzai, the Afghan president, has ratified laws imposing new draconian Taleban-era restrictions on women may also shake Western confidence in the moral authority of a military operation that has already lasted more than seven years and shows no sign of ending.

Britain, as the second-biggest contributor of troops to the war, has previously indicated that it is doing enough already and suggested other countries to carry a bigger share of America's burden.

But Sir Richard Dannatt, the head of the Army told The Times last week that as many as 2,000 additional British troops had been "earmarked for Afghanistan" and could be deployed swiftly depending on the political will.

The issue is causing tension within the Government which wants to be seen as backing Mr Obama's ambitious global agenda while also acknowledging that a war-weary public and the state of Treasury finances may mitigate against any further investment of British blood and money.

Both Mrs Clinton and General James Jones, Mr Obama's national security adviser, yesterday denied that they had given up on getting more Nato soldiers for the fight against a Taleban insurgency in Afghanistan.

"We have a national election coming up" said Gen Jones, referring the looming presidential election in Afghanistan. "Allies are considering how they might reinforce themselves and their forces. So I expect there will be additional troop contributions "

A Ministry of Defence spokeswoman last night said it expected that any formal request for further troops would be made the summit in Strasbourg where Mr Obama arrives with other Nato leaders today. Downing Street also suggested it was expecting the US would "challenge Nato to step up to the plate”. While aides stressed that some demands for extra firepower might be for the election period only, they acknowledged that any requests would likely cover some troops needed for could longer term operations.

In Strasbourg, a senior Nato official said that while Mr Obama's emphasis would be on financial investment and training teams to support the US military operation, "if the Americans wanted any ally to offer more troops for Afghanistan it would be the British".

Another source added: "An increase of 20 per cent in British troops would be a demonstration that Mr Brown truly believes in the special relationship which is not about forging new financial deals but about people who pull triggers."

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