However, he said the group would not agree to a ceasefire until foreign forces were withdrawn from Afghanistan.
And while the relationship between the Taliban and al-Qaeda has ebbed and flowed over time, at present, militants from al-Qaeda in the Indian Subcontinent (AQIS) are embedded in Taliban units and serve as trainers and advisers.
The Taliban said the Moscow meeting - their most significant with Afghan politicians in recent memory - would discuss the withdrawal of foreign troops, peace terms and its vision for governance.
The head of the delegation, who is in Russian Federation for talks between Taliban and opposition politicians, was quoted as saying no agreement had been reached with Washington on a timeframe for a troop pullout, but that he hoped it would happen soon.
Many Afghan women fear that their rights enshrined under the constitution will be given away as part of a peace settlement with the Taliban. He's also pressed for talks to bring together all major parties in the conflict.
Addressing the conference, Abbas Stanikzai, head of the Taliban delegation flayed the Afghan Constitution and the presence of the foreign troops in the war-ravaged country.
In January, they reached what Mr Khalilzad termed as a "draft framework" of an agreement.
The Taliban, responding to Trump's speech, rejected any suggestion of a lingering US focus on counter-terrorism after troops are drawn down, reiterating their long-held demand that all foreign troops get out.
Abdullah Abdullah, the country's chief executive, said Monday that the Afghan government should be at the center of any peace talks, adding that Kabul "would prefer the Moscow meeting had a different shape".
A broader second group of "legitimate stakeholders and opportunistic spoilers" - including regional powers like Russia, China and Iran - have their eyes keenly on waning United States influence in the region, Moradian added.
The Taliban ruled Afghanistan in 1996-2001 with a fundamentalist and often brutal interpretation of Islamic law.
"The important thing is we don't bargain about positions here, we bargain about the fact that women in Afghanistan are respected, as equal human rights holders, and I think that was important that they listened to this voice". THey were armed with modern weapons to launch quick attacks, he added.
Stanakzai said: "And today's discussion as we said before, it was very good, in a good atmosphere and fruitful".
President Ashraf Ghani has repeatedly called on the Taliban to begin direct negotiations with his representatives, but so far the group has refused, dismissing them as puppets of the US. For years the refusal of the United States to meet with Taliban officials has prevented any negotiation. "If we look at the Afghan issue in broader terms, we will see that there is a need to search for a political solution apart from resolving security issues".
"It is common knowledge that a dialogue between the Afghan government and the Taliban can not be avoided", he added.
Several delegates urged the Taliban to start talks with the Afghan government as intra-Afghan dialogue is the best option to end the conflict.
The conference is convened by the Afghan diaspora and is not a follow-up to the Moscow format on settling the crisis in Afghanistan, the latest meeting of which was held in November 2018. "But if that does not happen, they still want to have the Russian option open which has now brought them closer to Ghani's biggest opponents".
Moscow seeks to reassert its influence in the region and probably would want a role in shaping any possible peace plan.