"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".