Mohammad Sohail Shaheen, the chief spokesman for the Taliban delegation, told reporters in the Russian capital Thursday that the meeting was the latest step in efforts to reach a peace settlement.
"We are satisfied, that was successful negotiations, and we hope to continue this tempo in the future," he said after the meeting, Presstv Reported.
The spokesman also repeated the Taliban demand that US-led forces leave Afghanistan for any possible peace deal.
"We will be firm: withdraw the foreign troops, we will be firm that there should be a stable government in Afghanistan and that all Afghans should have participation in future government."
Shaheen went on to say that a ceasefire proposal had been discussed during the talks.
One member of the Taliban delegation also said Russian officials as well as religious leaders and elders had asked for a ceasefire.
"Still some more meetings to take place in this regard but most probably we may not announce a ceasefire," he said.
Speculation has been growing that the Taliban could agree to a temporary ceasefire over the three-day Eid al-Adha holiday, marking the fasting holy month of Ramadan next week.
The meeting in Moscow was opened on Tuesday by Russian Foreign Minister Sergey Lavrov, who said his country sees peace as the only possible scenario of settlement in Afghanistan.
Speaking on the sidelines of the conference, Taliban delegates reiterated their position that no ceasefire could be possible while foreign forces remained inside Afghanistan.
Mohammad Karim Khalili, the head of the Afghan High Peace Council the main body charged with pursuing peace efforts, said dozens of people were being killed in fighting every day and it was time for a "dignified and just mechanism" to end the bloodshed.
Even as the meetings took place, an attack in Kabul that killed at least six people underlined the violence that continues unabated across the country.
Separately, Afghan special forces freed 28 people held in a Taliban prison in the southern province of Zabul.
In recent months, the Taliban have stepped up attacks in their so-called spring offensive amid direct talks with the United States, rejecting calls by US chief negotiator Zalmay Khalilzad to lay down arms.
A sixth round of talks between the US and Taliban recently ended in the Qatari capital Doha with no tangible progress.
The Taliban have said peace negotiations were stumbling over the fundamental question of when foreign forces would depart the war-ravaged country.
The Taliban have been talking for months with US diplomats to agree the withdrawal of more than 20,000 foreign troops from Afghanistan.
The administration of President Donald Trump is now negotiating with the Taliban in an attempt to discourage the group from attacking US troops.
Moscow appears to be gaining influence in the ongoing process. Last month, the US announced that Washington had reached a consensus with China and Russia on the key formula for a peace deal it is negotiating in Afghanistan.
The Taliban’s five-year rule over at least three quarters of Afghanistan came to an end following the US invasion in 2001. However, 18 years on, Washington is seeking truce with the militants, who still control large swathes of land in the country.