The two leaders agreed that relations between their countries would continue after NATO troops are pulled out by the end of 2014, Karzai told a joint news conference.
Komorowski is expected to visit Polish troops in the insurgency-hit southern Ghazni province for an update on the transition process which will see Afghan forces take control of security when Polish soldiers leave.
The Polish president, who is travelling with Defence Minister Tomasz Siemoniak, told the news conference that Poland`s troops would remain in Afghanistan until the NATO deadline of end-2014.
"The Polish and Afghan friendship that was forged under very difficult conditions will definitely last longer than the presence of the last Polish soldier on the Afghan soil," he added.
There has been pressure in some European countries for an early withdrawal after NATO troops were targeted by their Afghan colleagues, particularly in the wake of the burning of Korans at a US military base late last month.
The US-led NATO force has 130,000 troops fighting the Taliban, who were toppled from power in a US-led invasion in 2001. (*)