Karzai discussed "issues of mutual interest" with Sheikh Hamad bin Khalifa alThani, state news agency QNA said, without giving details of the meeting in Doha city.
The Afghan president previously opposed a Taliban office in Qatar since he feared that his government would be frozen out of any future peace deal involving the extremists and the United States.
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 operation to oust the Taliban from Kabul in 2001.
But with US-led Nato combat troops due to withdraw from Afghanistan by the end of 2014, Karzai recently backed the proposed office in Doha and his office said he would raise the plan on Sunday.
Any future 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.
"We will discuss the peace process, of course, and the opening of an office for the Taliban in Qatar," presidential spokesman Aimal Faizi told AFP before Karzai left Kabul on Saturday.
"If we want to have talks to bring peace to Afghanistan, the main side must be the Afghan government's representatives - the High Peace Council, which has members from all the country's ethnic and political backgrounds," Faizi added.
Negotiating with the Taliban regime that harboured al Qaeda before the 9/11 attacks was for many years anathema to countries in the UN-backed coalition against the militants.
But the search for a political settlement became a priority as the insurgency raged on, with Taliban leaders able to fuel violence from safe havens across the border in Pakistan.
Kabul has repeatedly stressed that it will only start talks if the militants break all links with al Qaeda and give up violence, and Faizi said any Taliban office in Qatar must be subject to strict conditions.
"It can only be an address where the armed opposition sit and talk to the Afghanistan government," he said. "This office cannot be used for any other purposes."
Karzai met Qatari investors on Saturday evening and encouraged them to invest in the country as it works to secure stability before Nato-led combat forces withdraw next year.
"The future of Afghanistan is guaranteed because our relations have expanded with America and other countries such as China, India and Russia," he said according to an emailed statement.
"Afghanistan has good opportunities and resources that we can share with you."
The United Nations last week welcomed news that Karzai would visit Qatar, and issued another call for the Taliban to come to the negotiating table.
But a Qatar office could mean little if the Taliban continue to refuse to negotiate with Karzai or with the government-appointed High Peace Council.
"The opening of the Taliban office in Qatar is not related to Karzai, it is a matter between the Taliban and the Qatar government," Taliban spokesman Zabihullah Mujahid told AFP.
"Our representatives who are already in Qatar won't see or talk to him."
The militants broke off tentative contacts with the US in Qatar a year ago after the failure of attempts to agree on a prisoner exchange as a confidence-building measure.
Pakistan, which backed the Taliban's 1996-2001 rule over Afghanistan and is seen as key to any workable peace deal, has expressed support for a Taliban office in Doha.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ