The Taliban must make a "decisive split" with al Qaida if a political settlement in Afghanistan is to be brokered, the Prime Minister said today.
In a joint press conference at Lancaster House in London with President Barack Obama, David Cameron said the US operation against Osama bin Laden represented a "strike right at the heart of international terrorism".
Mr Cameron said the next 12 months represented a "vital year" in Afghanistan, while British and American troops had "broken the momentum of the insurgency" in the country.
In the Taliban heartland of Kandahar and central Helmand, the insurgents were "on the back foot", the Prime Minister said.
Calling for a political settlement, he told the press conference: "Now is the moment to step up our efforts to reach a political settlement.
"The Taliban must make a decisive split from al Qaida, give up violence and join a political process that will bring lasting peace to that country.
"We are agreed to give this the highest priority in the months ahead."
President Obama said Nato forces were "preparing to turn a corner" in Afghanistan.
He and Mr Cameron "affirmed the importance of beginning the transition to an Afghan lead for security this year and completing that transition by 2014".
Mr Obama added: "We discussed the opportunity that exists for promoting reconciliation and political settlement, which must be an Afghan-led process.
"President Karzai has made it clear he will talk to anyone who is willing to end the violence, split with al Qaida and accept the Afghan constitution."
The US president said he and Mr Cameron welcomed co-operation between Afghanistan and Pakistan.
He added: "The Prime Minister and I both agree that our nations have a long-term interest in ensuring that Afghanistan never again becomes the launching pad for attacks against our people.
"Alongside our allies and Nato partners, we are committed to a strong and enduring relationship with the people of Afghanistan."
Mr Cameron said he and Mr Obama had some "very good discussions" on security issues. Both Britain and America had suffered at the hands of terrorism, he said.
Recalling his own experience of 9/11, he told journalists: "My wife Samantha was in Manhattan on 9/11 and I will never forget the five hours of trying to get hold of her and she will never forget the New Yorkers she met that day or the sense of solidarity that she felt that day and we have felt ever since that day.
"Today, as we come up to its 10th anniversary, we should remember the spirit of that city and the sympathy we feel with those who lost their loved ones.
"There are those who say that this terrorist threat is beyond our control and we passionately believe that is wrong. We can defeat al Qaida and the events of recent months give us an opportunity to turn the tide on their terror once and for all."
He said Britain and America had to continue to work with Pakistan in the fight against terrorism, saying "their enemy is our enemy".