"Mullah Omar should come to Afghanistan and open a political office wherever he wants," said Karzai. "But he should drop the gun. He and his friends should come and make a political party. Do politics in this country, stand in elections. If people vote for them, it's theirs and they should take on the leadership of the country."
Speaking to reporters Thursday in Kabul, Karzai said the two sides could start peace talks based on common ground.
"What do they want? American and foreigners should leave Afghanistan? Yes, that what we too want. But come and sit with us, so we can send them back as soon as possible. If you have demands that are justified and demands about religion and country, you are most welcome," Karzai added.
The Afghan president has repeatedly called on the Taliban to stop fighting against coalition and Afghan forces, renounce violence and participate in a peaceful reintegration into society. But the Taliban refuses to negotiate with the Karzai administration, calling it a "puppet regime" of the international coalition.
Earlier this year, Taliban negotiators reportedly met with U.S. officials in Qatar for a series of discussions on possibly launching peace talks. But in March, the Taliban announced it was suspending any such discussions until, as it said, "the Americans clarify their stance on issues," including a prisoner swap.