Senior Afghan politicians and Taliban peace negotiators are expected to attend a two-day meeting in Moscow this week.
The potential May 28-29 meeting comes amid efforts to launch talks between the Afghan government and the Taliban after a planned summit in Qatar was canceled last month.
Taliban spokesman Zabiullah Mujahid said in a May 27 statement that a 14-strong Taliban delegation, led by deputy leader Mullah Abdul Ghani Baradar, will attend a ceremony on May 28 marking the establishment of diplomatic relations between Russia and Afghanistan.
The delegation would also meet Afghan politicians and elders the following day to discuss the future of the country, Mujahid said, without giving details.
It was unclear if Afghan government officials would attend the Moscow meeting.
The Taliban has said it will not negotiate with the Western-backed Kabul government, which it deems illegitimate.
Former President Hamid Karzai is set to attend the meeting, his spokesman has said.
Taliban officials met a delegation of powerful Afghan power brokers in Moscow in February, but those talks did not include members of President Ashraf Ghani's government.
Those talks marked the most significant contact between senior Afghan political figures and the militant group since the U.S.-led invasion in 2001.
The meeting in Moscow comes amid a push by the United States for a peace settlement with the Taliban.
Zalmay Khalilzad, the U.S. envoy seeking a peace deal with the Taliban, has held several rounds of talks with the militants in Qatar in recent months. The sides have made progress but have been unable to finalize a peace agreement.
In recent years, Russia has emerged as a power broker in Afghanistan, where the Soviet Union fought a disastrous war from 1979-89.
In November, Russia also hosted talks between the Taliban and Afghan political figures.
Khalilzad welcomed Russia's efforts in the peace process, although some U.S. officials have claimed that Moscow is promoting itself as a power broker to challenge the U.S.-backed peace process with the Taliban in Qatar.