Hollande was strongly criticised at a NATO summit last weekend for accelerating France's withdrawal of its roughly 3,400 troops in Afghanistan to the end of this year, two years ahead of the timetable agreed by the alliance.
"The mission of fighting terrorism and chasing out the Taliban is close to being accomplished, and this is something we can be very proud of," Hollande told journalists at an outdoor press conference in Karzai's garden palace.
"We will stay in Afghanistan but with a different role, our cooperation will focus on civilian fronts," he said.
The drawdown , a promise to voters during Hollande's election campaign following s uccessive attacks by rogue Afghan soldiers on French me ntors, breaks with the NATO timetable for a withdrawal of most foreign combat troops by the end of 2014.
It raised concern that other alliance nations may follow France's example and accelerate their withdrawal plans, handing security pr ematurely to fledgling Afghan forces.
At last weekend's meeting of NATO allies in Chicago, German Chancellor Angela Merkel criticised the early withdrawal, saying she wanted a unified pullout under the alliance's existing strategy of "in together, out together".
Some 2,000 French troops are due to leave this year but some will remain to provide support and training, and to look after equipment. France has 14 helicopters, 900 vehicles and 1,400 containers that need to be taken out via road and plane.
Visiting French forces at their base in volatile Kapisa province, Hollande t hanked t hem for what they had done for France and Afghanistan, a nd pr omised th e pullout would be "o rderly" and do n e in "close coordination with France's allies".
He also paid homage to the 83 French soldiers killed in the war, now dragging into its 11th year.
"The time has come for Afghan sovereignty. The terrorist threat that targeted our territory has not completely disappeared, b ut it has been partially suppressed," Hollande said.
France has been asked to contribute just under $200 million a year for long-term funding for Afghanistan, part of an annual bill estimated at $4.1 billion to maintain Afghan forces after 2014. Hollande has signalled that he will commit to nothing until it is clear how the money will be managed.
As well as training Afghan forces, France could also set up a medical college and some kind of cultural or archaeological centre, Hollande said, as well as aid the Afghan government with hou sing, energy, oil research an d crucial ag riculture aid .