The Afghan and Pakistani presidents are in Britain for talks on how to prevent a Taliban resurgence in the region when foreign troops withdraw.
David Cameron is hosting Hamid Karzai and Asif Ali Zardari at Chequers, the Prime Minister's country residence.
The formal meeting follows a private dinner on Sunday night.
It is expected to concentrate on how Pakistan and the international community can support the Afghan-led peace process.
This is the third round of talks since last summer when the trilateral discussions were initiated at the request of both nations.
Foreign ministers, chiefs of Army staff, chiefs of intelligence and the chairman of the Afghan High Peace Council are due to attend for the first time.
Foreign Secretary William Hague said the goal was to help the two nations "build closer co-operation around their common interest in a secure future".
But ahead of the summit, Mr Karzai questioned the motives of Western forces ending their mission in his country.
The leader raised the prospect of forces being drawn down because international leaders had realised the mission was mistaken.
He told the Guardian and ITN: "They feel fulfilled with regard to the objective of fighting terrorism and weakening al Qaida, or they feel that they were fighting in the wrong place in the first place, so they should discontinue doing that and leave."
The president said the greatest threat to peace was not insurgents but the interference of foreign powers, though he did not specify a particular country.
He said: "There will not be peace in Afghanistan by having an agreement only between us and the Afghan Taliban.
"Peace will only come when the external elements involved in creating instability and fighting, or lawlessness in Afghanistan, are involved in talks."
He claimed Helmand had been more peaceful before US troops arrived there in 2006 and predicted fighting would lessen once foreign troops leave next year.
He said: "The exit of foreign forces will not bring more violence for them to perpetrate against their own people, but a serious, strong, good reduction in violence will occur."
However, he conceded stability in the country would take longer to establish as the Afghan police and army continue to struggle against the Taliban.
And he admitted the government would not survive without western military and financial aid following the end of the Nato mission.
A Downing Street spokeswoman said: "As the Prime Minister has set out previously, a stable Afghanistan is not just in the interests of Afghans, but also in the interests of their neighbours and the UK.
"We share the same vision for Afghanistan: a secure, stable and democratic country that never again becomes a haven for international terror.
"We are working together to achieve it and Afghanistan's neighbours have a vital role to play. It is vital not just for the future security of their citizens, but for their prosperity too."