David Cameron met President Karzai at the PM's country residence
David Cameron has held a meeting with the Afghan President Hamid Karzai, his first with a foreign leader since becoming UK prime minister.
Both leaders agreed they wanted to "further strengthen" relations between their countries.
The talks were held at Chequers, the prime minister's country residence.
President Karzai stopped over in the UK on his way back from Washington, where he discussed issues with US President Barack Obama.
Downing Street said President Karzai's stopover was "an opportunity for early discussions" following on from previous meetings when Mr Cameron was leader of the opposition.
Officials also said it was President Karzai who had requested the meeting with the new prime minister.
A Downing Street spokesman said the pair discussed President Karzai's "very successful" visit to Washington and the prospects for the peace gathering - or jirga - in Afghanistan at the end of May.
"Both the president and prime minister agreed that the relationship between Afghanistan and Britain should be further strengthened," he said.
"The president and the prime minister expressed their admiration for the courage and skill of the British military in Afghanistan, and the sacrifices that British forces have made."
BBC diplomatic correspondent Bridget Kendall said President Karzai would be keen to establish for himself what relations with the new British leader and new coalition government might be.
"His relations with the previous Labour government were on occasion strained. And in earlier interviews, David Cameron's enthusiasm for President Karzai has sometimes been less than fulsome," she said.
"But in the last few days Mr Cameron has already been swift to reaffirm Britain's commitment to the mission to build a secure and stable future for Afghanistan."
Mr Hague says the UK and US should "take stock" on Afghanistan
Afghanistan was top of the agenda on Friday when Foreign Secretary William Hague met his US counterpart Hillary Clinton in Washington.
He told BBC Radio 4's Today programme it was going to be a "crucial year" for Afghanistan.
"Progress is being made but now we have to see an effective political process as well," he said.
"And that's what the United States has been working so hard on this week and that's where our efforts in our British relations with President Karzai and his government will come in over the coming weeks in a strongly co-ordinated way."
Mr Cameron will hold further discussions at Chequers with Defence Secretary Liam Fox, national security adviser Sir Peter Ricketts and service chiefs.
Mr Fox has indicated he will put additional pressure on some of Britain's EU partners to make greater contributions to the Nato effort in Afghanistan.
Mr Fox said the UK was in Afghanistan for "national security reasons"
Britain has about 9,500 troops deployed in Afghanistan, engaged in fighting the Taliban on the frontline in Helmand province and training the Afghan army and police.
In comparison, Germany's troop contribution is 4,665 personnel, France's is 3,750 and Italy's is 3,300.
Mr Fox told the Sun: "It is unreasonable to expect Britain to carry such a full burden inside the Nato alliance. We need to find better ways of burden sharing."
The new defence secretary declined to set a date for the completion of Britain's mission in Afghanistan.
"We are in Afghanistan for reasons of our national security," he said.
"We need to succeed if we are to deal with the terrorist threat. There are lots of other things to do in Afghanistan on democracy, human rights. But they are in addition to our military mission.
"We have to be clear that success in our military mission means the Afghan security forces need to contain the threats. Our job has to be to train Afghan forces so that can happen."