The meeting on Friday demonstrated Moscow's renewed aspirations in Afghanistan nearly 30 years after the Soviet Union withdrew its battered forces.
In his address, Lavrov said all countries of the region and the entire worldwide community would like to see Afghanistan as a peaceful, independent and prospering country, free of terrorism and drug trafficking.
"America does want to and needs to leave Afghanistan but we need to leave the Afghan government in charge and not to let the return of Taliban", former naval intelligence officer John Jordan told RT, adding that Afghanistan has turned into "a problem that everyone wants to solve but no one wants to own".
"Our participation at the meeting will be at the non-official level", he said.
Representatives from Iran, China, Pakistan, Tajikistan, Uzbekistan and Turkmenistan arrived for the talks, officials said.
"I hope that the efforts by Mr. Khalilzad will continue as it is, so that we will witness tangible results", said Maisam.
USA officials have held two meetings with the Qatar-based Taliban negotiators since July. Kabul, for its part, sent a 4-member delegation of its High Peace Council (HPC), which has been tasked with the reconciliation process.
For the first time, the meeting of regional officials on ways to end the war included a Taliban delegation, as moves towards achieving a political settlement pick up.
However, the High Peace Council, which did hold brief direct talks with the Taliban delegation in Moscow, did not officially represent the government, the Afghan Foreign Ministry said, but even this small rapprochement was regarded as success by all parties.
Taliban spokesman Mohammed Suhail Shaheen declined to specify the number in their delegation, but five Taliban representatives were present at a roundtable in the conference hall, and beforehand, up to nine people were seen.
Taliban said it is not ready for direct talks with the Kabul government and will negotiate with the United States instead, Russia's Interfax news agency quoted Sher Mohammad Abbas Stanakzai, head of the Taliban delegation, as saying.
Sources privy to the discussions Friday told The Indian Express that the Indian representatives - former Indian ambassador to Afghanistan Amar Sinha and former Indian High Commissioner to Pakistan T C A Raghavan - did not make any statement on behalf of New Delhi at the meeting.
At the end of October, Mujahid noted that the five high-level Taliban members transferred from the American prison in Guantánamo to Qatar in exchange for U.S. Army deserter, Sgt. Bowe Bergdahl will be among the group's representatives negotiating peace from Qatar.
Ministry of External Affairs spokesperson Raveesh Kumar on Thursday confirmed the participation and said, "Our participation at the meeting will be at the non-official level".
Maria Zakharova, a spokeswoman for the Russian foreign ministry, revealed on the eve of Friday's conference that delegates from 12 countries, including the United States, will attend the second "Moscow format consultations".
The meeting drew considerable criticism from Kabul as it did not involve the Afghan government.