The Prime Minister has made a direct appeal to the Taliban to enter peaceful talks on the future of Afghanistan.
David Cameron has been hosting talks at Chequers with Afghan President Hamid Karzai and Pakistani President Asif Ali Zardari, which he said had led to "an unprecedented level of co-operation".
Britain and Afghanistan have agreed to sign up to a strategic partnership between the two in the autumn.
They have also approved opening an office in the Qatari capital Doha for negotiations between the Taliban and the Afghan High Peace Council.
The Prime Minister said the agreement should send a clear message to the Taliban, adding: "Now is the time for everyone to participate in a peaceful, political process in Afghanistan."
He said: "This should lead to a future where all Afghans can participate peacefully in that country's political process."
Mr Karzai described the discussion as "very frank and open".
He echoed Mr Cameron's appeal to the Taliban to join peace talks, and said he hoped the previously strained relations with Pakistan could in future be "very close, brotherly and good neighbourly".
Mr Zardari said his country would fully support any dialogue with the Taliban, adding: "Peace in Afghanistan is peace in Pakistan. We feel that we can only survive together."
The Pakistan president also agreed along with his Afghan opposite number to strengthen co-ordination of the release of Taliban detainees from Pakistani custody to support the peace process.