"The Afghan people keep asking for more and more security forces in Afghanistan," he said, "not so much as a measure of physical security, but as a measure of international guarantees of commitment of staying with Afghanistan."
Blair said there was a limit to what British troops could do in Afghanistan.
"Our leadership is there but it's for a limited period," Blair told a news conference in his Downing Street office. "But of course we will be working and discussing with other countries as to how we make sure the security force continues. We will be there to give logistical support to the force which takes over from us."
Britain wants to end its command of the 17-nation mission in Kabul by the end of April. Muslim Turkey has said it has been asked by other countries to take over command of the force but has not yet made a decision.
Chancellor Gerhard Schroeder backed away on Thursday from a suggestion by his spokesman that Germany might assume the leadership of the foreign forces in Afghanistan.
Karzai reminded Blair and other world leaders they can't forget about Afghanistan as he says they did several years ago, or the country could fall into chaos.
CBS News Correspondent Sam Litzinger reports Karzai received a warm welcome, as he spoke to Blair's cabinet and met privately with the prime minister to discuss the huge rebuilding job facing his fledgling government.
"We will make sure that money is spent correctly in Afghanistan, in the right way, and that corruption is not seen in it," he promised.
He said Afghanistan would still be an occupied country were it not for the U.S.-British military campaign against the Taliban and Osama bin Laden's terrorist network.
"I thank you for that, and I thank the people of Britain through you," he told Blair at a joint news conference. "Britain, and other members of the international community...came to help us to fight our war against a horrible, horrible force, a force that knew nothing but to torture, kill and destroy lives."
"They did that in Afghanistan, they also did that in the most glaring, shocking, unbelievable way in New York last September."
Karzai thanked Blair for Britain's leadership of an international security force in Afghanistan, which now numbers about 2,500 troops.
Karzai made a similar plea for an broadened security force at the United Nations on Wednesday.
Blair said Britain's troop commitment would be limited in time and numbers, but he promised to stand by Afghanistan.
"Our role in that (force) has to be limited...but of course we will be working and discussing with other countries as to how we make sure that the security force continues...and does the work that peopl in Afghanistan want it to do," the prime minister said.
Karzai's stop in London followed a trip to the United States, where he met with President George W. Bush in Washington and addressed the U.N. Security Council in New York. He sat in U.S. First Lady Laura Bush's VIP box during her husband's State of the Union speech in Congress.
He planned to spend the night in London and fly home to Kabul Friday.
Karzai met privately with Blair before the news conference, and also spoke to a cabinet meeting at the prime minister's Downing Street office, one of the few foreign leaders invited to do so. Former U.S. President Bill Clinton was another.
He told cabinet members that the U.S.-led military campaign had given Afghanistan back to its people.
"We had lost it and now we have it," he said.
Blair also raised the issue of illegal drugs, telling reporters that Afghanistan had been the source of about 90 percent of the narcotics coming into Britain, and pledging to work with Karzai to cut off opium production.
"To be able to bring about a situation in which Afghan agriculture is focused on mainstream agriculture, not the poppy trade, is obviously of tremendous significance and importance," he said.
Karzai said he was committed to ending poppy cultivation and drug trafficking, and asked for international help to do so.
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