'Modern' Afghan state
Sarkozy said that the 1,900 French troops in Afghanistan would remain in the country for as long as needed.
"It is absolutely necessary that Afghanistan does not become a state which falls in the hands of terrorists, as we saw with the Taliban"
Nicolas Sarkozy, French president
"It is absolutely necessary that Afghanistan does not become a state which falls in the hands of terrorists, as we saw with the Taliban," Sarkozy said after the talks.
"That is why it is important that we help with the emergence of an Afghan state that is legitimate, democratic and modern."
The European nation is also due to send about 50 army instructors to Uruzgan to help train Afghan soldiers, in addition to about 150 it already has in Kabul.
France has been repeatedly urged by Nato members to dispatch more forces away from Kabul to eastern and southern areas, where fighters from the Taliban are more active.
The Taliban were removed from power in 2001 after a US-led campaign following the 11 September attacks.
During talks with Karzai in Kabul, Rudd said he assured the Afghan leader that Australian troops would remain in the country.
"Over the next several months, I would also be encouraging other friends and partners and allies in Nato to continue their commitments to this country and where possible extend them," he said following his meeting with Karzai.
Owen Fay, Al Jazeera's correspondent in Kabul, said the situation was in contrast to that of Iraq, where all Australian combat troops are to be withdrawn by next year.
Australia has just under 1,000 troops serving in Afghanistan as part of the Nato-led International Security Assistance Force (ISAF).
It suffered its first combat death in the country in October this year. There are about 60,000 international soldiers in Afghanistan, of which two-thirds form part of ISAF.