With US-led NATO combat troops due to withdraw from Afghanistan by the end of 2014, Karzai recently backed a proposal for the Taliban to open an office in Doha, the Qatari capital.
The militants refuse to have direct contact with Karzai, saying he is a puppet of the United States, which supported his rise to power after the military offensive that ousted the Taliban from power in 2001.
During the visit, the president was to meet Qatari officials "to discuss Afghanistan's peace process and bilateral relations between the two countries", Karzai's office said in a statement.
But in the television interview during his last visit to Qatar in March, Karzai said a Taliban office in Doha could pave the way for "direct contacts" and push forward the peace process.
Any peace talks still face numerous hurdles before they begin, including confusion over who would represent the Taliban and Karzai's insistence that his appointees should be at the centre of negotiations.