Obama's call "was good news because this has been the stand of the Afghan government," Karzai told a gymnasium full of Afghan women during a speech to commemorate International Women's Day.
Obama said in an interview with The New York Times published on Sunday that there may be opportunities to reach out to moderates in the Taliban, but the situation in Afghanistan is more complicated than the challenges the American military faced in Iraq.
Karzai warned that there are Taliban fighters who are beyond reconciliation - those who have joined with al-Qaeda, for instance. But he said talks should go forward "with those who are afraid to come back to their country, or who feel they have no choice but to stay with the Taliban for various reasons. They are welcome."
In the latest violence, a roadside blast killed a NATO service member and wounded two US coalition members in eastern Afghanistan on Sunday, the NATO-led force said. The alliance did not disclose the troops' nationalities or the exact location of the attack, but the majority of troops in eastern Afghanistan are American.
Another roadside blast in central Ghazni province hit a police vehicle, killing three officers and wounding another three, said Ismail Jahangir, the spokesman for the provincial governor.
The string of deaths continues an upward spike in violence that has spread throughout Afghanistan the last three years even as Obama's administration is trying to come up with a new approach to dealing with the Afghan war.