Mr Brown said his Afghan counterpart had offered to send 10,000 extra Afghan troops to be trained in Helmand, where most of the British forces were based.
There would also be 10,000 more Afghan police in Helmand and Kandahar, he said.
Asked about corruption in the Kabul administration, Mr Brown said Mr Karzai would present plans, including improvements to governance, to a conference in London next month.
Mr Karzai said he was "very, very sorry" when he saw British troops killed or wounded in Afghanistan.
He addressed the parents of British soldiers killed in Afghanistan, saying: "I am terribly sorry for them losing their sons and daughters, as we are sorry for us losing our sons and daughters in Afghanistan.
"But we have a job to do together and we must endure, as hard as it may be."
During his visit, he revealed that British forces had destroyed almost 1,500 roadside bombs in the last six months.
This, said Brigadier Dickie Davis, the Isaf chief of staff for southern regional command, might provoke a further backlash from the Taliban.
Asked whether Afghan forces would be in a position to take over the control of security in the country, Brig Davis was non-committal.
The prime minister slept in these "basic quarters" at Kandahar air base
But he stressed that there had been "remarkable progress" within the Afghan National Army.
Meanwhile Defence Secretary Bob Ainsworth has said the Ministry of Defence faces "tough decisions" over funding.
He told BBC 1's Politics Show that other areas of defence would face cuts as limited resources were shifted to support the operation in Afghanistan.
"I am being asked to live within my budget and there are tough decisions that will have to be taken in that regard," Mr Ainsworth said.
It is reported that Mr Ainsworth will this week announce the closure of at least one RAF base and a scaling back of the UK sovereign base area in Cyprus, as well as cuts to the MoD Police and back office functions.
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