Afghan President Hamid Karzai and his Pakistani counterpart Asif Ali Zardari are set to hold key talks on Monday with British Prime Minister David Cameron on the Afghan peace process.
The summit at Cameron's Chequers country retreat near London is aimed at boosting cooperation between Afghanistan and Pakistan, amid growing fears that a civil war could erupt when international troops leave Afghanistan next year.
"This trilateral process sends a very clear message to the Taliban - now is the time for everyone to participate in a peaceful political process in Afghanistan," a British government spokeswoman said.
Support from Pakistan, which backed Afghanistan's 1996-2001 Taliban regime, is seen as crucial to peace after NATO troops depart - but relations between the neighbours remain uneasy despite some recent improvements.
Both Kabul and Washington have regularly accused Pakistan of helping to destabilise Afghanistan.
But Afghan peace negotiators have welcomed Pakistan's release of dozens of Taliban prisoners in recent months, a move they believe could help bring militants to the negotiating table.
Cameron hosted a private dinner for Karzai and Zardari at Chequers on Sunday evening, ahead of Monday's in-depth talks between the leaders and their officials.
These are the third trilateral talks in a year following meetings in Kabul in July and New York last September - but they are the first in which Pakistani and Afghan army and intelligence chiefs will also take part.
In an interview with Britain's Guardian newspaper and ITV television station released late Sunday, Karzai said the biggest threat to peace in Afghanistan was not the Taliban, but meddling from foreign powers.
"Peace will only come when the external elements involved in creating instability and fighting, or lawlessness in Afghanistan, are involved in talks," he said, without naming any particular country.
The president also suggested Western troops had been "fighting in the wrong place" in Afghanistan, saying security in the southern Helmand province was better before British troops arrived there.
A statement released by his office said the talks in Britain would be "focused on ways to accelerate peace process in Afghanistan and further strengthen cooperations between Afghanistan and Pakistan in the fight against terrorism and extremism".
Karzai is also due to meet the heir to the British throne Prince Charles during his three-day trip to Britain, which began on Saturday.
Britain still has around 9,000 troops in Afghanistan ahead of a scheduled withdrawal in 2014.
Afghan soldiers and police are taking on responsibility for battling Taliban militants from the 100,000 NATO troops due to depart by the end of next year.
But more than 60 foreign soldiers were killed in 2012 in "insider attacks" by members of Afghanistan's security forces, which have bred mistrust and threatened to derail the training process.
Afghan forces are also increasingly being targeted by Taliban bombers as they take on a greater security role.