British Prime Minister David Cameron was due to hold talks in Kabul with President Hamid Karzai and Pakistani Prime Minister Rajaz Pervez Ashraf, officials said.
The first meeting between the three leaders comes as Britain, along with its NATO allies, prepares to withdraw its troops from Afghanistan by the end of 2014.
"The meeting, which will take place shortly, will be about tripartite relations, regional security, the war on terror and Afghanistan's peace process," a spokesman for Karzai, Siamak Herawi, told AFP on Thursday.
Relations between Afghanistan and Pakistan have traditionally suffered from distrust and mutual blame for Taliban violence plaguing both countries.
Kabul has asked Islamabad to assist efforts to broker a peace deal with the Taliban, whose leaders have traditionally had close ties to Pakistan, but the militia has said it broke off contacts with the Americans and refuses to talk to Karzai's government.
Cameron is also expected to sign a deal to build an officer's training academy modelled on Britain's Sandhurst as Afghan forces take over increasing responsibility for the fight against Taliban insurgents.
On Wednesday, Cameron visited frontline troops in the southern province of Helmand, where British forces are based at Camp Bastion.
Britain has around 9,500 troops in Afghanistan, making it the second-largest contributor to NATO's US-led 130,000-strong International Security Assistance Force, which is due to withdraw by the end of 2014.
Asked about reductions in troop numbers, Cameron said it would be done in "a sensible, ordered, practical way -- 9,500 to 9,000 this year.
"As Afghan troops take a bigger role we will be able to reduce troop numbers further next year.
"I don't want to see some cliff edge. I'm confident we are going to have a staged reduction and deliver a safe and secure situation," he said.
It is the Pakistani prime minister's first visit to Kabul since being elected last month after his predecessor was dismissed for contempt, and the first time he holds talks with Karzai and Cameron.
An Islamabad government official said he will raise the issue of cross-border attacks on Pakistan from Afghan territory and press for increased security measures to prevent such incursions in future.
Afghanistan shares a disputed and unmarked 2,400-kilometre (1,500-mile) border with Pakistan, and Taliban and other Al-Qaeda-linked militants have carved out strongholds on either side.