UK PM David Cameron signed a deal to build an officers' training academy modelled on Sandhurst.
It was President Karzai's first meeting with Pakistan's new Prime Minister, Raja Pervez Ashraf.
Afghanistan is facing the withdrawal of international troops in 2014, and received $16bn (£10.3bn) in aid pledges at a conference earlier this month.
The Afghan economy relies heavily on international development and military assistance. The World Bank says aid makes up more than 95% of Afghanistan's GDP.
The BBC's David Loyn in Kabul says it was Mr Cameron's idea to hold the unusual three-sided meeting, believing that Britain, Pakistan and Afghanistan share a common enemy.
Mr Cameron said Britain will remain committed to Afghanistan after combat troops come home in 2014, and that the Taliban should not think that they could "wait it out".
He said the pull-out would be carried out "in a sensible, ordered and practical way". Five-hundred UK troops are due to be withdrawn from Helmand Province this year, leaving 9,000.
"As Afghan troops take a bigger role we will be able to reduce troop numbers further next year," Mr Cameron said.
He also stressed Britain's continuing commitment to development aid to Afghanistan beyond 2014.
'Fruitful results'
Our correspondent says that behind the warm handshakes between the Afghan and Pakistani leaders there is deep suspicion - each side openly accuses the other of fomenting terrorist attacks across the mountainous frontier region that divides them.
President Karzai said the formation of the academy for officers was a step towards strengthening and professionalising Afghanistan's forces, leading to the establishment of a trained and well-equipped national army.
He thanked Britain for the assistance it has provided to Afghanistan and for the sacrifices made by young British soldiers.
"I am confident that it will produce fruitful results," he said. "I hope that the pains you suffered will result in the establishment of a developed and self-sufficient country."
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