The prime minister, Tony Blair, today said that Britain had a "complete and continuing commitment" to Afghanistan, but made no mention of expanding Britain's role in the international peacekeeping force.
Hamid Karzai, the country's interim leader, said an extension of the force was a "demand of the Afghan people" at a joint Downing Street press conference with the prime minister, adding that Britain could be proud of its contribution at the head of the troops.
"The Afghan people are really asking for these forces as a symbol of the commitment of the international community," he said.
Mr Blair did not promise to extend Britain's contribution in terms of troops - which now stands at 5,000 soldiers - but said he believed that the international community had a long-term commitment to the force. His spokesman said that any decision to expand its role was a matter for the interim government and all countries with soldiers involved.
The two men - who met previously at Bagram airbase near Kabul - also discussed the drugs trade and tourism. Mr Karzai thanked Britain for its role in the US-led war against Osama bin Laden's al-Qaida network and the Taliban.
"Afghanistan could not have been freed from the occupation of terrorism, from the presence of terrorism, without the help of the friends that we have, without the presence of your troops there, without the sacrifice they made, and without the contribution you made," he said.
Mr Blair said the last remaining members of the Taliban and Bin Laden must still be found, but spoke of the humanitarian work and reconstruction needed in the country.
Mr Karzai flew into London this morning and was met at Heathrow airport by the foreign secretary, Jack Straw.
The two men headed to Downing Street, where the Afghan leader joined ministers for the end of their weekly cabinet meeting - one of few foreign leaders to have done so.
He thanked ministers for their contributions to reconstructing his nation, still devastated after three decades of war. Britain has pledged to spend £200m over the next five years.
"We will make sure that the money that your taxpayers have given to our government is spent respectfully and correctly," Mr Karzai said.
He again outlined his spending priorities - education, health, road building, communications and banking. He said the Taliban had run away with whatever money they could get their hands on.
"We literally had no currency notes. Our own notes, which are printed in trillions," he laughed.
As well as financial aid, Britain may agree to provide support in the future in the form of a military training team to help build up a regular Afghan army.
Mr Karzai had caught an overnight flight from Washington, where he had been offered US military expertise in training Afghan troops by the US president, George Bush. Mr Bush also extended $50m (£35m) in credit facilities to Afghanistan.
While in the US, Mr Karzai reopened his country's Washington embassy, which has been closed for the last five years, and attended Mr Bush's state of the union address on Tuesday night.
However, Mr Bush ruled out the possibility of US troops joining the small international peacekeeping mission in the country, despite repeated invitations from Mr Karzai.
The White House spokesman, Ari Fleischer, said: "The president's philosophy is that the United States should not be overly deployed in peacekeeping around the world. The purpose of the troops should be to fight wars."
Mr Karzai also addressed the UN security council yesterday, asking for an expanded international presence to keep growing lawlessness in check and to provide the stability needed for reconstruction.
