Karzai went from Washington after a high-profile visit to soothe ties with US President Barack Obama, whose administration has been critical of Karzai for failing to battle corruption that many say is hurting US-led efforts to fight the Taleban.
Afghanistan was high on the agenda when new Foreign Secretary William Hague, a former Conservative leader who lost to Tony Blair in the 2001 election, met his US counterpart Hillary Clinton in Washington on Friday.
Britain is the second-largest troop contributor to NATO-led forces in Afghanistan with 9,500 troops based mainly in southern Helmand province, where scores of British soldiers have been killed since the war started in late 2001.
Last year, a record 108 British troops were killed in Afghanistan, according to independent website icasualties.org.
The British military has struggled against Taleban insurgents in Helmand and the former Labour government was criticized for failing to provide soldiers adequate equipment.
"Our immediate priorities are making sure that we get to grips with Afghanistan and tackling nuclear proliferation (in) Iran," Hague told The Times newspaper this week.
