Afghan and Pakistani Presidents Hamid Karzai and Asif Ali Zardari today set a six-month time-frame to achieve a peace settlement for Afghanistan following trilateral talks with UK Prime Minister David Cameron.

"All sides agreed on the urgency of this work and committed themselves to take all necessary measures to achieve the goal of a peace settlement over the next six months," they said in a joint statement after the talks hosted by Cameron at his Chequers country retreat near London.

Cameron appealed to the Taliban to join the peace talks on the future of Afghanistan after the summit which was attended by top spy and military generals from the three countries.

Zardari said that Pakistan would fully support any such dialogue involving the Taliban. "Peace in Afghanistan is peace in Pakistan. We feel that we can only survive together. We cannot change our neighbourhood or our neighbours," he said, speaking alongside Cameron and Karzai.

Karzai said he hoped relations with Pakistan – which have been strained in the past – could in future be "very close, brotherly and good neighbourly".

Cameron also announced the opening of an office in the Qatari capital of Doha for negotiations between the Taliban and the Afghan High Peace Council.

"Now is the time for everyone to participate in a peaceful, political process in Afghanistan. This should lead to a future where all Afghans can participate peacefully in that country's political process," he said.

The three leaders noted significant progress since they last met in September 2012 and stressed the importance of maintaining the pace and momentum.

According to the joint statement issued by the British Prime Minister's office at 10 Downing Street here, President Zardari reiterated that Pakistan would extend "full support to peace and reconciliation" in Afghanistan.

It added: "The Afghan and Pakistani delegations agreed that the quality of dialogue and cooperation had significantly improved".

"They committed themselves to continue to make strenuous efforts in the spirit of mutual interest. Both sides agreed that good neighbourly relations between Afghanistan and Pakistan, that ensured the long term stability of both countries, was of fundamental importance".

They also agreed to "arrangements" to strengthen coordination of Taliban detainee releases from Pakistani custody in support of the peace and reconciliation process.

Both Pakistan and Afghanistan said they looked forward to a joint conference of Afghan and Pakistani Ulema in early March.

"The two sides agreed that they wanted to build greater trust and cooperation between their military and security services and agreed concrete steps to deliver this.

"The Afghan and Pakistani chiefs of defence staff and intelligence enjoyed fruitful discussions and agreed on new mechanisms for strengthening co-operation," the statement added.

The talks, held in the relatively secluded ambience of the British PM's country retreat in Buckinghamshire, were part of a trilateral process launched last year and followed a private dinner for Zardari and Karzai last evening.

It involved senior military and intelligence figures, including the UK's chief of defence staff, General Sir David Richards, and MI6 Chief Sire John Sawers, for the first time.

This is the third round of discussions since Cameron instigated the three-way process in 2012, when the three leaders met in Kabul and New York.

With the NATO withdrawal expected in 2014, Karzai has said that he does not want a repeat of the mistakes made when Russia withdrew from Afghanistan a quarter of a century ago, plunging the country into civil war.

"We share the same vision for Afghanistan – a secure, stable, democratic country that never again becomes a haven for terrorism.

"Clearly there is much more work to be done in the months ahead and the United Kingdom will continue to stand firmly behind both countries as they work together to bring stability to the region," Cameron added.