"We discussed the subject of direct talks with the Taliban and asked them to choose the place and the starting time", said Ehsan Tahiri, High Peace Council spokesman, according to Russia's RIA news agency.
Any peace process in Afghanistan with the U.S. boots on the ground is impossible, the Taliban delegates said after a meeting in Moscow, adding that the current Afghan government is a United States puppet stalling the talks.
The Afghan government and the Taliban both denied that the conference marked direct negotiations for peace.
Representatives from the Afghan militant group joined the talks on Friday to which Russia's invited a dozen countries.
For his part, HPC represantive Eshan Taheri said that Kabul was ready for direct talks with the group.
In August, the Afghan government announced that Afghanistan and Russian Federation would co-chair proposed future talks in Moscow on Afghanistan's peace.
"The INC believes that the Afghan peace process should be Afghan led and Afghan driven and unfortunately the Afghan government is not on the table in Moscow", Congress leader Manish Tewari told The Hindu.
Western officials and Ghani's government view the Moscow meeting with some suspicion as an attempt by Russian Federation to push its way into a process they say must be led by Kabul.
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Russian Federation seeks to promote "inclusive, inter-Afghan dialogue" to try to resolve Afghanistan's 17-year civil war, Foreign Minister Sergei Lavrov said at the opening of the conference.
"With participation in the meeting, the global status of the Islamic Emirate [the Taliban] will be strengthened even further Such diplomatic efforts of the Islamic Emirate showcase the active, clear and independent diplomacy and policy of the Islamic Emirate in the political field", asserted the insurgent spokesman. "The meeting in Moscow helped move things in this direction".
The development marks a major shift in New Delhi's policy as this is the first time ever that India will attend a forum in which the Taliban will be present.
Taliban spokesman Zabiullah Mujahid said the militant group was sending five representatives, who will not hold "any sort of negotiations" with the Peace Council delegation.
"The fact that the Afghan government did not send an official representative sends a message that they are not fully committed to these talks", Yuri Barmin, a fellow with the Russian International Affairs Council, told Al Jazeera on Friday. The U.S. embassy in Moscow sent its first political secretary, Jacob Choi, to observe the event. United States troops have been fighting in Afghanistan since the 2001 invasion that was launched to dismantle al-Qaida and topple the Taliban.
Meanwhile, the Prime Minister Narendra Modi-led government faced questions from Opposition leaders on its surprise decision to attend the meeting, a turnaround from its position on Russia's September 4 proposal for a meeting, which India had declined.
The meeting came at a sensitive time.
Newly appointed United States peace envoy Zalmay Khalilzad has been trying to convince the Taliban to agree to negotiate an end to the war and there are fears the Russian meeting could derail those efforts. "It is clear that on the way to this goal it is necessary to overcome a lot of obstacles, including mutual grievances and mistrust accumulated by the parties", he said, adding that the objective of the talks was to create conditions favourable to "direct negotiations between the [Ghani] government, the Taliban Movement and representatives of the country's broad public and political circles".