The meeting marked the first time the Afghan government and Taliban meet for direct talks at a high level.
The Russia-managed Afghan peace talks, or the "Moscow Forum", will also feature representatives from China, Pakistan, the US, Iran, Afghanistan and several other central Asian countries, as per Russian officials.
Speaking at a press conference Sher Mohammad Abbas Stanikzai, a Taliban representative, said the group would first discuss issues concerning the U.S. with the Americans and emphasized that their main demand was the withdrawal of foreign troops.
"Their participation in today's event is meant to make an important contribution to efforts to create conditions for direct talks between the government, the Taliban movement, public and political circles". This time around, Afghanistan's government has announced a four-member team from its High Peace Council for the event.
Footage released from the meeting shows that in addition to representatives of the High Peace Council, Afghanistan's former ambassador to Moscow Abdul Qayum Kochi was also at the meeting.
"Our expectations are to talk to the Taliban members at this meeting", she said.
North Atlantic Treaty Organisation chief Jens Stoltenberg had said Tuesday that Afghanistan´s chances for peace were "greater now" than in many years, even as the Taliban step up attacks on Afghan forces, which are suffering record high casualties.
Russian Federation is hosting the talks for peace in Afghanistan and has invited several countries including India, the US, Pakistan and China.
The US, which is leading a separate push from Russian Federation for helping a speedy recovery of Afghanistan, will send staffers from its embassy in Russian Federation.
The deputation of two former officials to the Moscow meet betrays New Delhi's dilemma over dealing with the situation in Afghanistan. It was for the Taliban and the Afghan delegation to answer, however, whether there will be any direct contact or interaction between the two sides, the Russian spokeswoman said when asked whether the two warring parties will have bilateral discussions.
Taliban spokesman Zabiullah Mujahid toldAFP news agency the group's five representatives will not hold "any sort of negotiations" with the delegation of Kabul administration.
The Afghan foreign ministry emphasised that the council did not represent the Afghan government at the meeting, however, but was acting as a "national" non-government institution. "We took a considered decision to attend the meeting at a non-official level", he said.
The Moscow talks also abruptly highlighted Russia's increased role in Afghanistan, 30 years after Soviet troops left the country following a disastrous war there.
"The Moscow format of talks is aimed at establishing an inclusive inter-Afghan dialogue in the interests of advancing the process of national reconciliation", Lavrov said as he opened the meeting that has brought together representatives of the Afghan authorities and the Taliban.
The Moscow conference comes as Washington already has initiated a direct dialogue process with the Taliban, meeting a long-running insurgent demand.
Stanikzai said the Taliban does not consider the current government in Afghanistan as legitimate.