The possibility of the Taliban opening a political office in Qatar is expected to be discussed, officials say.
The setting up of an office in Qatar is regarded as an important step in formalising a channel for peace talks between the Afghan government and the Taliban.
US-led Western troops are due to leave Afghanistan by the end of 2014.
As the Afghan president’s visit began, there were reports that two children and nine suspected Taliban militants had been killed in an air strike by international forces close to the south-eastern city of Ghazni.
A Nato spokesman quoted by Reuters news agency said an Afghan police patrol had come under attack and had called in a helicopter for support.
Last month, President Karzai issued an order banning Afghan security forces from calling in foreign air strikes in residential areas, because of heightened tensions about the extent of civilian casualties.
Mr Karzai’s office said the talks in Qatar would focus on bilateral cooperation and on Afghanistan’s peace process.
Last month Mr Karzai and Pakistan’s President Asif Ali Zardari said that they would work towards a peace deal for Afghanistan within six months.
Previous talks between the Taliban and the US have run in to difficulties, with the Taliban suspending talks in March last year.