American officials are to meet with representatives of the Taliban for the first time, in peace talks led by the Afghan government.
The two sides will meet in the Qatari capital of Doha, where the Taliban set up an office on Tuesday, the BBC reported.
David Cameron, speaking from the G8 summit in Northern Ireland, voiced his support for the meeting.
The prime minister said the UK had been "engaged and involved in this process right from the start", and that it was "the right thing to do".
Mr Cameron said: "I have long argued that we need to match the security response in Afghanistan... with a political process to try and make sure that as many people as possible give up violence and give up armed struggle and join the political process.
"That is exactly what I hope can happen with elements of the Taliban. That is the point of the Taliban office in Qatar. That is the point of the discussions that the Americans will have.
"We have been fully engaged and involved in this process right from the start, indeed from the moment I became Prime Minister.
"I think this is the right thing to do."
Mr Cameron acknowledged that it would be difficult to speak with the Taliban, but drew parallels with the peace process in Northern Ireland itself.
"Of course it involves all sorts of difficulties," he said. "But in the end, we are standing in a place where people who were once committed to violence decided to give up that violence and join the political process, and that is what is required in Afghanistan."
He added: "That shouldn't signal any weakening of our security response - it absolutely doesn't. But if we can persuade people that there is a legitimate political path they can follow, we should do so."
Afghan president Hamid Karzai has said a High Peace Council will travel to Qatar to chair the talks, which are expected to take place in the coming days.
Representatives of the Taliban leader, Mullah Omar, are believed to be ready to sever ties with Al Qaeda by opposing "the use of Afghan soil to threaten other countries", the Guardian said.
However it is likely the US will demand more in order for talks to go ahead and will press for a denunciation of violence and recognition of women's rights.
The announcement coincides with Nato handing over sole responsibility for the country's security to Afghan forces after a war lasting over 12 years.
Despite the positive developments three civilians were killed on Tuesday in a bomb attack on a prominent lawmaker, reports AP.
He survived but the casualties are a stark reminder of the reality of the conflict on the ground.
For a number of years American commanders have acknowledged the war could not be won on the battlefield alone and some degree of dialogue with the Taliban would be necessary.
President Barack Obama is believed to have informed other world leaders at the G8 Summit on Monday night.
A previous attempt last year to reconcile the two sides broke down when the US backed down on a promise to release Taliban detainees from Guantanamo Bay.Suggest a correction