David Cameron and Barack Obama today insisted that British and American troops were on course to step back into a support role from next year.
After talks in the White House, the Prime Minister and president said the international mission was entering its final stages ahead of the Afghans taking full responsibility for security in 2014.
Their confident pronouncements on Afghanistan came as both men lavished praise on each other and reaffirmed their commitment to the US-UK relationship, Mr Obama describing it as "essential", "indispensable" and "the strongest that it has ever been".
"There are some countries whose alliance is a matter of convenience but ours is a matter of conviction; two states... united for freedom and enterprise, working together day in, day out, to defend those values and advance our shared interests," Mr Cameron said.
At the press conference Mr Obama in turn described Mr Cameron as an "outstanding ally, partner and friend".
The PM and his wife Samantha were earlier welcomed to Washington with an extravagant ceremony at the White House.
On a sun-drenched South Lawn, packed with 7,000 guests - including children from both nations - Mr Cameron was given a 19-gun salute and a review of troops.
Mr Obama was emphatic about the enduring value of what he terms the transatlantic "essential relationship".
"Our world has been transformed over and over and it will be again," said the president.
"Yet through the grand sweep of history, through all its twists and turns, there is one constant - the rock-solid alliance between the United States and the United Kingdom.
"The reason is simple - we stand together, we work together, we bleed together and we build together, in good times and in bad, because when we do, our nations are more secure, our people are more prosperous, our world is a safer and better and more just place."
He added: "Our alliance is essential, it is indispensable to the prosperity and security that we seek not only for our own citizens but for people around the world."
Mr Cameron responded that the relationship between the US and UK had produced "the most powerful partnership for progress that the world has ever seen".
"When the chips are down, Britain and America know we can always count on each other, because we are allies, not just prepared to say the right thing, but to do the right thing and to do it in the right way," said Mr Cameron.
Both leaders were keen to stress how they had deepened their personal relationship with a trip to watch basketball in Ohio last night. Mr Cameron joked that he had learnt some new words - "alley-oops, brackets and fast breaks" - and might even install a hoop in 10 Downing Street.
At the press conference, the Prime Minister said he would get his "own back" by taking Mr Obama to a cricket match and "explaining the rules to you and some of the terminology you will have to try and get straight, as I tried last night".
The Camerons made a present to the Obamas of a customised Dunlop table tennis table, a reminder of a game the two men played on the president's visit to the UK last year.
On Afghanistan, the two men confirmed that international forces would shift into a support role from next year.
Mr Cameron said that recent days - including the deaths of six British soldiers in a roadside explosion and the killing of 16 Afghan civilians, including several children, by a US soldier - were a reminder of how high the cost of war had been for Britain, America and Afghanistan.
"We are now in the final phases of our military mission," he said.
"That transition to Afghan control, as agreed at Lisbon, is now well under way. And next year, as the president said, in 2013, this includes shifting to a support role.
"This is in advance of Afghans taking full responsibility for security in 2014."
He added that the situation was "considerably improved" and that the target of transition to full Afghan control in 2014 was "achievable".
"We want Afghanistan to be able to look after its own security with its own security forces so we are safe at home," he said.
"That's the key, that's the message we need to keep explaining to people. But I think what we are trying to do by the end of 2014 is achievable and do-able."
Mr Obama said the details of the next stage of transition to Afghan control would be determined at the Nato summit in Chicago.
He insisted there would remain a "robust" military presence inside Afghanistan over the next year to send a clear message to the Taliban.
But he said it was unlikely there were going to be "any sudden additional changes to the plans we currently have" over troop withdrawal.
The president said the US would begin implementing a "long-awaited defence trade treaty" with the UK from next month.
"This will put advanced technologies in the hands of our troops and it will mean more jobs for workers in both of our countries," he said.
The leaders also agreed "nothing is off the table" in the approach they will take to tackling the growing crisis in Syria.
Mr Cameron said the current EU-wide oil embargo had "dramatically increased pressure" on President Bashar Assad's murderous regime but the UK and US were prepared to go further.
He added: "We are serious about the talks that are set to resume but the regime has to meet its international obligations.
"If it refuses to do so, then Britain and America, along with our international partners, will continue to increase the political and economic pressure to achieve a peaceful outcome to this crisis.
"The President and I have said that nothing is off the table."
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