Mullah Abdul Ghani Baradar, who headed the militant group's delegation, said in an eight-minute audio tape of an interview posted Thursday that the latest marathon talks will pave the way for future progress.
“We are very hopeful for the peace talks, because the latest round had some good dialogues which paved the way to more progress regarding peace in the future,” he said.
Baradar went on to reassure Afghans that any political settlement wouldn’t herald the return of the Taliban rule and its strict laws.
“If (Afghans) think of us like brothers I trust in God that all the problems will be solved,” the Taliban leader said, adding, “I ask all our countrymen to be sure there is no need to worry. Everyone will be treated very well.”
He also gave assurances that the Taliban would not allow their homeland to be used again by foreign militant groups to mount terrorist attacks in other countries, Presstv reported.
“We assure the neighboring, regional and other countries that the upcoming system will not be against anyone, we are not under the influence of anyone, and have no aim of harm to anyone.”
Elsewhere in his remarks, Baradar offered a message to Taliban fighters, saying that even though he felt the group had achieved military victory over the US-led forces, they should remain composed and not become arrogant.
Baradar, a co-founder of the group, was released from a Pakistani jail last year to participate in the talks. He is believed to be widely respected by the Taliban's various factions, with analysts saying his participation would help garner support for any deal from insurgents on the frontlines.
The latest round of talks in Qatar lasted 16 days and finished on Tuesday.
In a series of tweets on Tuesday, US special peace envoy Zalmay Khalilzad, who led the US delegation in Qatar, said that it was "clear all sides want to end the war." Further talks are expected later this month.
The Taliban have said they want an agreement on four issues for any deal to be signed, including the US troop withdrawal from Afghanistan. The other issues are counter-terrorism assurances, intra-Afghan dialogue, and a ceasefire.
A senior Taliban commander, familiar with the talks, said the group will announce a ceasefire with the US only after foreign forces leave the country.
The US has entered into talks with the Taliban to end its 18-year war in Afghanistan.
The marathon talks last month saw the US and the Taliban walk away with a "draft framework" focused on a potential US troop withdrawal and a pact to prevent Afghanistan from harboring terrorists.
The Taliban have reiterated opposition to direct talks with President Ashraf Ghani's administration in Kabul. Ghani has repeatedly stressed that no peace deal between the Taliban and the United States could be finalized without involving his government.
The Taliban's five-year rule over at least three quarters of Afghanistan came to an end following the US invasion in 2001 but 18 years on, Washington is seeking truce with the militants.
President Donald Trump has said he intended to reduce the number of US forces in Afghanistan.
The US forces have remained bogged down in Afghanistan through the presidencies of George W. Bush, Barack Obama, and now Trump.