Italy has lost 10 soldiers in Afghanistan, one of them an intelligence officer wounded when Italian and British troops freed him and a colleague from capture by fighters in September.
Ten people had died in the operation - nine of the abductors, said by Afghan police to be Taliban fighters, and an Afghan interpreter.Unpopular presence
After the incident, one of the communist factions within Prodi's government called for the withdrawal of Italian troops from the country.
Support for the mission has been waning in some of the nearly 40 nations in the Isaf force - consisting of about 40,000 people working with Afghan security forces and a US-led coalition of about 20,000 mostly US troops.
Prodi's visit to the country follows visits by the leaders of France and Australia, who met Karzai on Saturday.
Each leader pledged that their countries were committed to Afghanistan for the long term.
Making the first ever visit to Afghanistan by a French president, Nicolas Sarkozy told Karzai that France has a long-term political and military interest in Afghanistan. 'Detestable signal'
Sarkozy said: "We did not want to give the signal of a withdrawal, which would have been a detestable signal at a time when we see the ravages that terrorism can do to the world."
"A war, a war against fanaticism is being played out here, that we cannot, that we must not, lose."
The European nation is also due to send about 50 army instructors to southern Uruzgan province 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 Karzai 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in Kabul, said the situation was in contrast to that of Iraq, where all Australian combat troops are to be withdrawn by next year.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 Isaf.
It suffered its first combat death in the country in October this year.