(CNN) -- British Prime Minister David Cameron arrived Saturday in Pakistan for talks with President Asif Ali Zardari about building a "strong relationship" between Pakistan and Afghanistan, the prime minister's office said.
Cameron acknowledged "difficulties" and "blocks in the road" to achieving that aim.
The UK leader is also to discuss the potential for British business in Pakistan's growing economy.
Cameron arrived from Afghanistan, where he made an unannounced visit Saturday and met with UK troops in Helmand province. He also spoke with Afghan President Hamid Karzai.
While visiting with Karzai, Cameron said his country has "a good relationship with Pakistan," the UK's Press Association news agency reported.
Speaking in Kabul at press conference with Karzai, Cameron added that "it's in Pakistan's short-, medium- and long-term interest to have a secure, stable and prosperous Afghanistan with which they have a good and strong relationship."
Pakistan-Afghanistan ties were "always difficult, there are always blocks in the road, but I know that the president will see past them," Cameron said.
Cameron's visit in Afghanistan coincided with Armed Forces Day, a series of events held across Britain on Saturday to recognize the contribution of the nation's servicemen and women, military veterans and their families.
Speaking after talks with Karzai at the presidential palace in Kabul, Cameron said the two nations had a "shared commitment to a strong partnership beyond 2014," the Press Association reported.
But Cameron stressed that Britain would be withdrawing all combat forces from Afghanistan by the end of 2014, from which point it will offer financial support and run an officer training academy.
There are currently 8,000 British servicemen and women serving in Afghanistan, alongside 68,000 from the United States, the largest contributor of troops.
The NATO-led international coalition formally handed over security responsibility to Afghan national forces 10 days ago.
They faced an early test of their capabilities Tuesday when a group of attackers stormed the entrance to the presidential palace in Kabul. The Taliban claimed responsibility for the attack in which three guards died, according to the government.
UK Gen. Nick Carter, deputy commander of the NATO-led coalition in Afghanistan, told Britain's Guardian newspaper Saturday that he believes the West should have tried talking to the Taliban in 2002, in the aftermath of the 2001 invasion, to help find a political solution.
U.S. Secretary of State John Kerry has cast doubt in the past week on whether potential U.S. peace talks with the Taliban in Qatar will happen.
The Taliban opened a Doha office this month with a promise to renounce international terrorism and commit to peace negotiations, conditions the United States had set before it would support establishing the office as part of peace talks.
Asked about the prospect of such talks, Cameron said the political process would only succeed "if those who are involved in the Taliban put down their arms and stop fighting," the Press Association reported.
The coalition's plan is to withdraw all international combat troops by the end of 2014 but to keep a residual force in the country to help train Afghans and carry out counterterrorism operations when needed. The size of that force remains under discussion.
CNN's Bharati Naik contributed to this report.