Stakes are high for the talks which follow a week of US-Taliban negotiations with both sides eyeing a peace deal.
Washington has said it wants to seal a political deal with the Taliban ahead of Afghan presidential polls due in September to allow foreign forces to begin to withdraw.
Security was tight at the luxury hotel hosting the intra-Afghan summit as around 70 delegates, who were required to surrender their phones, filed into the hall. They sat in a vast semi-circle facing a large video screen and the hosts from Qatar and Germany.
"Gathered around the table today are some of the brightest minds representing a cross-section of Afghan society," said Markus Potzel, Germany's special representative for Afghanistan and Pakistan.
"Each of you will have a unique opportunity and a unique responsibility to find ways of turning violent confrontation into a peaceful debate," he said as he opened the gathering.
Taliban negotiator Abbas Stanikzai had a brief altercation with a security guard as he attempted to enter the secure conference area.
"We want to go to the dialogue but they are not letting us," Stanikzai said to an officer, who replied: "we are not joking with you, stop shouting at us".
But he and the rest of the Taliban delegation, which included Suhail Shaheen, the group's Doha office spokesman, took their seats in the expansive ballroom shortly before the talks began at 0630 GMT.
The discussions concluded just after 1500 GMT, two delegates said, and were due to resume on Monday morning.
Qatari Foreign Minister Mohammed bin Abdulrahman Al-Thani tweeted that he looked "forward to a constructive dialogue".
The so-called intra-Afghan meeting follows six days of direct US-Taliban talks that have been put on hold for the two day Afghan conference and are set to resume Tuesday, according to both sides.
Delegate Asila Wardak, a member of the High Peace Council established by former president Hamid Karzai to engage with Taliban elements, told AFP "everybody is emphasising on a ceasefire".
Wardak added that Stanikzai spoke about the Taliban's position on "women's role, economic development, (and) the role of minorities". He mentioned they "will allow women to work, to go to school and study -- based on Afghan culture and Islamic values", she said.
US Secretary of State Mike Pompeo tweeted that the Afghan gathering "has been a long time coming" and praised the country's "government, civil society, women, and Taliban" for coming together.
US lead negotiator Zalmay Khalilzad said Saturday that the latest round of US-Taliban talks "have been the most productive of the rounds we've had with the Talibs".
The Taliban said they were "happy with progress".
The United States is not participating directly in the two-day Afghan summit, which is being attended by political heavyweights, government officials and at least six women.
The Taliban, who have steadfastly refused to negotiate with the government of President Ashraf Ghani, have stressed that those attending are only doing so in a "personal capacity".
Ghani's administration, which the Taliban consider a puppet regime, has also been excluded from the direct US-Taliban talks.
Sunday's gathering is the third such meeting following landmark summits in Moscow in February and May.
An agreement with the Taliban is expected to have two main pillars -- a US withdrawal from Afghanistan and a commitment by the militants not to offer sanctuary to jihadists. The Taliban's relationship with Al-Qaeda was the main reason for the US invasion nearly 18 years ago.
But the thorny issues of power-sharing with the Taliban, the role of regional powers including Pakistan and India, and the fate of Ghani's administration remain unresolved.
The Taliban, believing they have the upper hand in the war, have kept up attacks even while talking to the United States and agreeing to the Afghan dialogue.
A Taliban car bomb in eastern Afghanistan killed at least 12 people and wounded scores more on Sunday, officials said.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.