The PM said he wanted to “further strengthen” relations between Britain and Afghanistan.
President Karzai was the first international leader to visit the PM since he became Prime Minister on Tuesday.
The visit came a day after Foreign Secretary William Hague held talks with US Secretary of State Hillary Clinton in Washington with Afghanistan topping the agenda.
A Downing Street spokesman said:
The Prime Minister was delighted to invite President Karzai to Chequers, the first formal visit by an international leader since the election.
They discussed President Karzai’s very successful visit to Washington, and the prospects for the peace 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.
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.
Following the meeting the PM held further discussions at Chequers with Defence Secretary Liam Fox, National Security Adviser Sir Peter Ricketts and service chiefs.